The Italian had been banned by football's world governing body Fifa over his role in transfer deals and finances while at former club Juventus.
“It's been a couple of weeks that Fabio was not here. So, it's not a shock, we are well prepared,” said Stellini, ahead of Spurs vital Premier League match against Newcastle United on Saturday.
“This has not affected preparations because Fabio was far from here for a couple of weeks, so nothing changes in this situation.
“But humanly we're very close to Fabio, all of us. It was a tough period for him and now the final result is very sad for everyone, for him and his family.
“Humanly we're very close to him. The club made a statement and this is all that I can say. It's a tough moment so I want to be close humanly with him. All my heart is with him but it's a tough moment so you can understand this period is tough.”
Fabio Paratici was banned from football for 30 months by Fifa over his role in transfer deals and finances while at former club Juventus. PA
Spurs chairman Daniel Levy will now take on the task of appointing Spurs' new manager and finding a replacement for Paratici.
Stellini is currently in temporary charge after Antonio Conte, who Paratici was instrumental in appointing as manager, left the North London club in March.
“This has been a stressful time for Fabio and his family. We wanted to ensure that we allowed for due process to be followed. Fabio is a man who lives and breathes football - we wish him well,” Levy said in a statement.
The turmoil off the pitch has overshadowed what is a crucial weekend in Tottenham's season as they take on fourth-place Newcastle at St James' Park.
The Magpies and three points ahead of Spurs who are fifth but Eddie Howe's side also have a game in hand on their rivals.
Last week saw Tottenham fall to a disastrous 3-2 home defeat to struggling Bournemouth that severely dented their top-four hopes.
Everton 1 Tottenham 1: Player ratings
EVERTON PLAYER RATINGS: Jordan Pickford - 6. Made the right decision by sticking out a leg to stop Porro’s cross from finding Kane in the sixth minute. His passing wasn’t as good as usual. PA
Seamus Coleman - 6. Saw his half-hearted shout for a penalty waived off by the referee in the first half. Made a crucial block to stop a Spurs counter-attack from a corner in the second half. Getty
Ben Godfrey - 7. Had a chance to score his first Everton goal in the 24th minute but was denied by a block from Dier. Could only manage a terrible cross when he had the chance to pick out Simms in the box late in the game. Credited with the assist for Keane’s equaliser. Reuters
Michael Keane - 9. Cleared Kane’s shot off the line in the ninth minute. The first-half hero turned villain in the second half as he was responsible for fouling Romero and giving away a penalty. But he became the hero again and sent the Everton fans into raptures by hitting a long-range shot into the top corner in the 90th minute. AP
James Tarkowski - 8. Made a crunching last-ditch tackle in the sixth minute to dispossess Skipp on the edge of the Everton penalty area. Almost won the game for the Toffees with a shot which was blocked in the 93rd minute. Getty
Idrissa Gueye - 7. Made an important interception to stop Hojbjerg from finding Kane with a through-ball in the eighth minute. Failed to trouble Lloris when he was set up on the edge of the Spurs penalty area in the 47th minute. Getty
Abdoulaye Doucoure - 3. Should have tested Lloris when he met a Gray corner in the 30th minute. Let his teammates and the fans down by flinging his arm at Kane’s face and picking up a needless red card. Getty
Amadou Onana - 7. Tested Lloris with a long-range effort in the 37th minute. Made a brilliant sliding tackle to dispossess Dier on the edge of his box and set up Gueye for a strike. Getty
Alex Iwobi - 7. Crucial to everything the Toffees created in the first half. His brilliant first touch and impressive ball-carrying ability caused serious problems for Spurs’ backline. Reuters
Dwight McNeil - 6. Showed his defensive awareness by sticking out a leg to deny Porro a simple tap-in in the 20th minute. Worked hard on the left flank to help keep Kulusevski and Porro quiet. Getty
Demarai Gray - 6. Had the first attempt of the match which he hit just over the crossbar. Saw his weak attempt get saved by Lloris in the 73rd minute. AP
Vitaliy Mykolenko (Coleman 76’) - N/A. Came on and helped the Toffees dominate proceedings on the left flank. AP
Ellis Simms (Gray 77') - N/A. A willing runner but hardly had a sniff after coming on. Reuters
Tom Davies (Onana 84') - N/A. Reuters
James Garner (Gueye 84') - N/A. PA
TOTTENHAM PLAYER RATINGS: Hugo Lloris - 6. Had several shaky moments in the first half with his mishandling of crosses. Made a number of saves after Kane’s opener to preserve Tottenham’s lead. Reuters
Cristian Romero - 7. Regularly joined the attack as Spurs sought to make their numerical advantage count in the second half. His foray forward paid dividends as he won the penalty for Kane to open the scoring. Picked up his customary yellow card in the 79th minute. AFP
Eric Dier - 6. Unknowingly made a crucial block with his face to stop Godfrey’s shot from troubling Lloris. Almost cost Spurs a goal when he was dispossessed on the edge of his penalty area just after the restart. AP
Clement Lenglet - 5. Outmuscled by Iwobi too easily in the 64th minute. Failed to provide adequate cover for the overlapping Perisic. AP
Pedro Porro - 6. Had an early attempt which was saved by Pickford’s outstretched leg. Caused panic among Everton fans when his inventive shot hit the side netting in the 72nd minute. AP
Ivan Perisic - 6. Almost set up the opener for Spurs but Kane failed to direct his header on target. Played a part in the eventual Spurs opener as his cross led to the penalty incident. Reuters
Oliver Skipp - 6. Took a little too long on the ball when he had the chance to play in Kane early in the game. Kept things simple in the middle of the pitch for Spurs. AP
Pierre-Emile Hojbjerg - 5. Played an excellent diagonal pass to Perisic in the 10th minute. Failed to close down Keane quickly for the Toffees equaliser. AP
Dejan Kulusevski - 6. The Sweden international was one of Tottenham’s better players in the first half as Spurs struggled to get behind Everton’s deep backline. Faded a little after the restart. PA
Son Heung-min - 5. The offside flag spared his blushes after he failed to beat Pickford when he was played through on goal by Kulusevski in the 43rd minute. Struggled to get involved in the second half. Getty
Harry Kane - 8. Unlucky to see his shot cleared off the line by Keane in the ninth minute. Should have at least got his header on target when Perisic’s cross found him in the penalty area. Sent Pickford the wrong way to open the scoring from the penalty spot in the 68th minute. Getty
SUBS: Davinson Sanchez (Lenglet 77’) - N/A. Made a superb block to deny Tarkowski in the 93rd minute. Getty
Lucas Moura (Son 82’) - 3. Gifted Everton a way back into the game by picking up an unnecessary red card in the 88th minute. Getty
Newcastle were also beaten, 3-0 at Aston Villa, meaning Spurs at least remain within touching distance.
But Aston Villa and Brighton, in sixth and seventh respectively, are breathing down the neck of Stellini's side, who face Manchester United and Liverpool over a crunch seven-day period.
And they first take on a Newcastle side that have lost just once on home turf all season, conceding just nine goals in 14 games.
“It's an important week because after this week we don't have many chances to change. This is a week in which if we want to change something we have to play well and get points,” Stellini said.
“We had one week to recharge after the last game, we had a good week and we're well prepared to play this game.
“It'll be tough because it's never easy in the Premier League. This is one of the worst stadiums to play in for the atmosphere's power, but we have a good squad and I believe in the players.”