Croatia coach Slaven Bilic lauded his team on Sunday for their 3-1 victory over the Republic of Ireland, saying they had opened the road to the quarter-finals, though he conceded that going further at UEFA EURO 2012 could be tough. "Tonight we showed that we can play," Bilic said after the final whistle in a rain-swept Municipal Stadium in the western Polish city of Poznan. "Maybe the Irish were the better team in some moments, but I think that if you look, the overall impression is that we were the much better team," the former Croatia defender said. "We are strong as a team, and I think that after this match we are getting even better and even stronger. I expect to play even better against Italy because the first match is the most difficult, and this is behind us." Bilic underlined that both teams had gone into the match fully aware that they had to perform. "I'm sorry for the Irish. They were looking for a chance in this match. But it was the same for us," he said. Earlier, in the Baltic port of Gdansk, heavyweights Italy and Spain had drawn 1-1, meaning Croatia top the table. "We have three points, and we're top of the group," said Bilic. "One win would be enough to go to the quarter-finals. We cannot fly in the championship, but let's go step by step. We respect all our opponents. "We have no fear against anyone. Spain and Italy are favourites in our group, but I still think we are able to beat one of them." Mario Mandzukic scored a double in the game, his first goal in the just the third minute to make it 1-0 and the second after the break to take the score to 3-1. "Mario's a top class player. He's playing at his top. Wolfsburg stayed in the Bundesliga thanks to him," Bilic said of the 26-year-old striker, who was named man of the match. Handing over the award, former Yugoslavia striker Predrag Mijatovic heaped praise on Mandzukovic. "Just go on like this, I'm sure you can score more goals in this tournament," he said. Mandzukovic said the game had been tough. "It was a hard match. We knew that it wasn't going to be easy," he said. "We did our best and I think we deserved a victory. It was very important that we scored an early goal," he added. It was not so easy on the pitch. They are really good fighters." Striking a personal note, he added: "My Dad asked me to score a goal with my head. I'm a really tall player and I like to have my chances." Forty-three-year-old Bilic, would, after six years in charge, like nothing better than to lift the trophy before he moves into club management with Russia's Lokomotiv Moscow. Like the Republic of Ireland, Croatia earned their EURO 2012 slot in the play-offs, in their case against Turkey - exacting revenge for Turkey's victory on penalties in the EURO 2008 quarter-finals. Their progress four years ago raised hopes of a return to Croatian football's 1990s glory days, when Bilic was a pillar of their defense. Croatia, emerging from the war sparked by the collapse of Yugoslavia, reached the quarter-finals of EURO 1996 and finished third at the 1998 FIFA World Cup™. FIFA .