Croatia took the early lead in Group C after beating a defensively-lapse Ireland side 3-1 in Poznan.
Croatia took an early lead courtesy of Mario Mandzukic, before Sean St Ledger temporarily brought Ireland level. But a goal just before half-time form Nikica Jelavic, followed by a second strike from Mandzukic saw Slaven Bilic's side run out comfortable winners.
Making their first finals appearance in a decade, Ireland showed signs of nerves early on. It was that edginess which played a part in some defensive hesitation that led to Croatia taking the lead just three minutes in.
Darijo Srna put in a deflected cross from the byline that found an off-balance Mandzukic 14 yards out. Able only to aim a tame header toward goal, it seemed that the danger would be averted, but the ball somehow beat a desperate dive from a slow to react Shay Given. Keith Andrews may have distracted Given as he opted to leave it for his goalkeeper, but the experienced number one will still be disappointed with his effort.
After going behind, Ireland began to settle and display an element of composure on the ball. And they got their reward as they brought themselves back on level terms after 19 minutes. Aiden McGeady whipped a dangerous free-kick toward the back post and St Ledger came in round the back of an unaware Vedran Corluka to apply the finishing touch with his head from close range.
Gradually Croatia began to assert some control on the match, with Modric pulling the strings in the middle of the park. The playmaker even forced a save from Given with a well-struck side-foot effort from 25 yards out that was just too close to Given.
Increasingly Ireland dropped deeper and deeper with both wide midfielders essentially operating as full backs. The withdrawn position of the Irish side meant that there was plenty of space for Croatia's midfielders to move into, a strong factor in Croatia going back in front two minutes before the break.
Modric had acres of room to fire in a shot that ricocheted off the cluster of players on the edge of the Ireland box. Once again showing the edginess in the Irish defense, Stephen Ward lashed at a clearance that merely traveled across goal, where Nikica Jelavic showed his poacher instincts to prod home over Given from six yards out.
Unfortunately for the Irish, veteran coach Giovanni Trapattoni's doubtless stern words at the break appeared to have little impact.
Just three minutes after the restart, Ivan Perisic's inswinging cross from the left once again caught the Irish defense too deep, allowing Mandzukic to get his head to the ball first. It was a formidable header from the striker, as he faced away from goal from fully 12 yards out, that struck the post before bouncing back onto a prone Given and into the net.
Realizing the scale of the task in front of them and the importance of getting back into the match, Trapattoni responded by bringing on strikers Jonathan Walters and Simon Cox.
Though, still struggling to create openings from open play, Ireland will feel incredibly hard done by that they were not awarded a penalty just past the hour mark. Receiving the ball right on the edge of the Croatian box with his back to goal, Robbie Keane was met with a stern challenge from Gordon Schildenfeld that went right through the back of Ireland's record goalscorer and left him apoplectic with rage at the referee's failure to award the spot kick.
Croatia, though, were still the more composed side in possession and, with 13 minutes remaining, they came close to making it four. Srna, in a typical foray forward from right-back, picked out Ivan Rakitic on the edge of the box, who met the ball with a well-struck first-time effort off his instep that curled just wide of the far post.
Ireland's best chance of getting back into the match always looked like being unsettling Croatia with a direct style and balls aimed quickly into the box. It was that method that saw them register an effort on target as Keith Andrews met a cross from the right with a header that proved comfortable for Stipe Pletikosa.
The same trick almost paid dividends once again in injury time. Andrews was well positioned as he met a corner from the right, but could only put his header wide of the target.
That was to prove the last hope for Ireland as time ran out on their efforts to make a comeback. And there could be little complaints at the final outcome. The defeat is likely to prove fatal to Ireland's hopes of qualifying for the quarter-finals with games to come against World and European champions Spain and an Italy side that looked far better than many predicted in their opening draw with the Spanish.
Setup with a strong focus on not conceding, Ireland were uncharacteristically poor in defense as they contributed in large part to their own downfall. But Croatia should not go without credit, having made the most of their opportunities with some clinical finishing. And with Modric a strong creative presence, linking up well with Perisic and Rakotic, Croatia may surpass their low expectations this summer.