In front of the hammer and sickle and beneath a fur cap, Richard Dunne's image looks out over Dublin's Aviva Stadium. The slogan on the banner reinforces the legend he created on that claustrophobic occasion in Moscow: The Iron Curtain. Nothing got past the Republic of Ireland defender in last September's 0-0 qualifying draw against Russia, which moved his country inexorably towards the Euro 2012 finals. His exploits in the competition have already been immortalised.

Dunne sits in the cigar room of the Grand Hotel in Sopot, the city on the banks of the Baltic Sea in northern Poland where the Ireland squad are based. The hotel is indeed exquisitely grand. Fine cigars and caviar are on show in one glass cabinet while vintage Dom Perignon bottles line up along a ledge. On the walls are portraits of the hotel's famous guests: Fidel Castro, Henry Kissinger, Greta Garbo. They look down from all walks of life. A black-and-white Brigitte Bardot movie projects silently on to another wall.

Adulation and grandeur, though, seem to sit uncomfortably with Dunne. Humility is his default setting. "Moscow was just a game," he says. "It's strange because I cleared one off the line but everyone did the same things. You train and you just end up in the right positions at the right times. It's not always as good as that."

Dunne neglects to mention the blocks and the headers and the tackles. Or the blood that he spilt, which necessitated a change of shirt. The new one lacked a number so the goalkeeping coach, Alan Kelly, seized a felt-tip pen to scrawl the No5 on the back. Dunne's "5uperman" jersey would become a prized charity auction item.

The 32-year-old describes the game of his life as a "blur" and not only because of the head wound that needed four stitches. His memories of Russia's visit to Dublin in October 2010 are clearer. The visitors had a sharper cutting edge that night and led 3-0 after 50 minutes. Although Ireland rallied to 3-2, Russia were impressive victors and Dunne gave vent to his emotions afterwards, telling reporters that Ireland's players needed to assume greater responsibility.

"People ask you questions in the heat of the moment and you want to say stuff," says Dunne. "We just needed to stop accepting second best, stop being this team that nearly gets there. We had to do it and to do it we needed to be stronger in those big games. It was just the frustration. After the France thing, this was a big chance to win our home games and we got hammered for an hour, really."

The France thing, when Ireland were denied qualification for the 2010 World Cup by Thierry Henry's infamous handball, will always haunt Dunne and his team-mates. But they are no longer the nearly team. Thanks in part to that hard-earned point in Moscow, and a favourable play-off draw against Estonia – whom they beat 5-1 on aggregate – they are here in Poland, with excitement mounting ahead of Sunday'sGroup C opener against Croatia. Dunne hopes there are more individual and collective heroics to come.

"The banner [at the Aviva Stadium] is pretty good, it's brilliant to walk out and have something like that," he says. "I appreciate it, but it's in the past. We're probably going to have similar battles in the games coming up. In every game, we have to produce the same performances and battle in the same way."

Dunne has waited his whole career to play at a major finals. He was a member of the 2002 World Cup squad, the last time Ireland qualified for a tournament, but was an unused substitute. He had no complaints, despite featuring regularly during the qualification campaign. Dunne had played the season at Championship level with Manchester City, having been relegated with them in 2000-01, and Mick McCarthy's more established centre-halves, Steve Staunton and Gary Breen, were fit.

It is different now. Dunne is the first name on Giovanni Trapattoni's team-sheet, at the heart of his miserly defence, and he has come to epitomise the values that the manager demands: focus, maturity and discipline. "You'd like to think that when you have a game like Moscow the opposition are never going to score, but as soon as you do, I guarantee that they will score," says Dunne.

He will need his very best form against the might of Spain and Italy, but first his focus is on Croatia, the team managed by Slaven Bilic, his former Everton team-mate, which boasts familiar and potent offensive threats. "Slaven was a really nice fella, really cool and chilled out," Dunne says. "He played the guitar. His side are like us. They'll be relaxed going into the games, rather than having any fear.

"Croatia are technically very good and Luka Modric is the one that makes them tick. I know, having played against and seen him at Tottenham for a long time, that he's one of the top players in the tournament. He's definitely one to stop, and so is Nikica Jelavic. He's done brilliantly since he joined Everton."

Dunne endured a trying season at Aston Villa, which took in a fractured shoulder that sidelined him for two months from February and a dogfight towards the bottom of the Premier League table. Relegation was avoided, but it was not enough to save the manager, Alex McLeish. He has been replaced by Paul Lambert.

"It was very hard for Alex McLeish because of his Birmingham connections," Dunne said. "The fans never took to him. He probably didn't get a fair go, but, as players, we weren't good enough. For the chairman and the fans, they needed a change as much as anything else, so hopefully now we can push on."

Going away on Ireland duty, where Trapattoni has been in charge for four years and consistency has been a by-word, might have felt like a release. The relaxed atmosphere in the squad, promoted by Trapattoni, was in evidence at their Gdynia training base during the week, before their flight to Poznan on Saturday morning. Trapattoni was the defender in a crossing and shooting drill on Thursday. "He's quite happy for us to have a laugh, as long as we do the hard work," Dunne says. "He plays a massive part in our spirit."

Dunne briefly turns his thoughts to the longer-term. This tournament has the feel of an international swansong for him, but he does not see it that way. "I'll be around next campaign, too," he says. "Fingers crossed, everything is OK."

It is the clash with Croatia that consumes him. The nerves are building, the pressure is intensifying. Dunne is ready.