Croatia may not have reproduced their swashbuckling performance of the play-off first leg in Turkey on Friday but few fans in a freezing Stadion Maksimir were complaining as they celebrated qualification for their fourth UEFA European Championship finals in five attempts since 1996.

After their commanding 3-0 away success, Croatia were overwhelming favourites to progress on Tuesday night. That meant the goalless draw was sufficient, so satisfaction at securing a berth in the finals, rather than joy, was the dominant emotion on show afterwards.

"We are glad we won through against a tough squad like Turkey," said playmaker Luka Modrić. "I think we deserved this qualification and that we belong there in the finals."

Goalkeeper Stipe Pletikosa concurred. "Turkey was a tough draw for the play-offs so we're happy with 3-0. It was a frozen pitch tonight and maybe some frozen play from us but we knew what our target was. They had a great chance in the first half, but after that we dominated and deserved to win."

Turkey needed to make an early dent in Croatia's aggregate lead and came within a whisker of doing so just five minutes in. Selçuk İnan's shot from distance bounced past Pletikosa and back off the post to Colin Kazım Richards just a few metres from goal. The FC Rostov goalkeeper's instinctive save from Kazım Richards's snapshot proved an early turning point in the game, denying Turkey a launch pad from which to claw back the deficit.

"We had a chance to score in the first half, in fact I had the chance," said the Galatasaray AŞ midfielder. "It was a reflex shot from me but the keeper did really well to save it. It was just too difficult for us to come back."

Rather than dwell on a failed mission, Kazım Richards preferred instead to accept defeat gracefully and look to the future with a positive mindset. "Now we will think about our World Cup qualifying games – that is our next goal," he said. "I want to congratulate the Croatian players. They deserve to go to the finals."

Croatia defender Josip Šimunić said UEFA EURO 2012 was a reward for the fans after a qualifying campaign which began well but at times threatened to become derailed. "The fans were great again tonight," said the GNK Dinamo Zagreb centre-back.

"We hope that a lot of them will support us at the finals. We received some criticism during our group games but in the end we managed to do it yet again – four times now out of five. I think this is really amazing for a country of just four million people."