Republic of Ireland's first ever appearance at the finals ended in defeat as Steph Catley's second-half penalty earned co-hosts Australia a 1-0 win in Sydney. Australia had suffered a blow before the game when captain Sam Kerr was ruled out of their opening two Group B matches – against Ireland and Nigeria – due to a calf injury sustained in training. The 29-year-old, Australia's all-time record scorer, hopes to be fit for the final group match against Canada on July 31. Ireland frustrated the Matildas in the first half but their good work was undone when Marissa Sheva pushed Hayley Raso and Brazilian referee Edina Alves point to the spot. Stand-in captain Catley converted from the spot in the 52nd-minute to seal three points for Australia. “It's incredible to get the win, I think this is the longest build-up to a game in my entire life,” Catley told reporters. “Losing a player like Sam, probably the best player in the world and her as a person, obviously we were heart-broken. We had to use her spirit … to help us push on. She's so, so important, she's our spiritual leader.” The opening game of tournament earlier in the day had seen the other host nation, New Zealand, shock Norway 1-0 in front of 42,137 fans in Auckland – a national record for any football match in the country, men's or women's. Australia's game had 75,784 fans watching at Stadium Australia in Sydney – a record attendance for a women’s football match in the country. “We knew this game would be tough,” said Australia manager Tony Gustavsson. “All the teams here will put up a fight. Everyone can beat everyone in this tournament. “Tournament football is always about finding a way to win. There's been a lot challenges thrown at this team over the last 24 hours, an opening game at a home World Cup and then you add Sam Kerr's injury to that. They stuck together and played as a team and that mental toughness I am proud of.” As for the Irish, their World Cup debut ended in defeat but there was much to be proud of. Megan Connolly, Katie McCabe and Louise Quinn all came close to what would have been a famous equaliser but the hosts held on for the win. “It is very disappointing,” said Ireland boss Vera Pauw. “We said at half time it would be a game decided by one mistake, whether it was us or them, and that is what happened. “Sam Kerr is one of the major top strikers of the world so her not playing was of course an advantage for us. They have such a powerful team, it was difficult for us to play against them but they did so well. They didn't create a lot of chances, right? “A draw would have been a reasonable result. I think everybody is proud that we are part of the top nations and we can only grow from this.”