Euro 2012 Watch: Tough night for Dunne and Given in Croatian loss
Ireland's prospects of progressing beyond the group stages suffered a huge blow as they were undone by the clinical Croatians in Poznan.
Mario Mandzukic's header eluded Given to put the Croatians ahead inside three minutes but a spirited Irish response saw Villa supporter Sean St Ledger equalise.
Nikica Jelavic's delightful dinked finish made it 2-1 before the break.
And a second Mandzukic header, which went in off Given, sealed the win.
It could have been different had former Villa loanee Robbie Keane been handed a late penalty when he appeared to be bundled over in the box - but the referee waved play-on and goodbye to their hopes in the opening encounter.
Manager Giovanni Trapattoni insists his side's Group C hopes are not over, however. Ireland play Spain on Thursday before meeting Italy on June 18.
"We have to believe," said the Italian. "This evening we met a strong technical team. But every game in this tournament can be a surprise."
St Ledger, who scored his country's goal on the night, believes Ireland can get a result against world and European champions Spain.
"It is obviously going to be tough, but that's football," he said.
"You are not going to go through tournaments unbeaten. You will lose some - Croatia are in the top 10 for a reason.
"There is no better game to come next than Spain. Obviously we will relish the challenge of the world champions, so why not go and get a result?"
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