The 73-year-old Italian concedes his team were overrun in the first half of their Euro 2012 opener, but also claims that the linesmen did little to help their cause
The former Italy manager must now hope that his team can get a result against both Spain and Italy if they are to reach the last eight of the competition, a task which seems unlikely given the poor start the Irish have made to their campaign.
Mario Mandzukic put the Croats ahead early on in the game before Sean St Ledger nodded home an equaliser for Ireland. But it was Croatia's controversial second goal that Trapattoni believes was the killer blow.
"We had a little reaction after the goal but the second goal was two metres offside, I said that to the referee," he told RTE Sport.
Trapattoni did admit, however, that his side were second best of large parts of the game.
He added: "They dominated the first [half], they had more possession, we were inferior in midfield.
“I think the first little mistake, [we were] too slow to come out of the box and the goal put us in a very bad situation, psychologically.”
After the first round of games, the Republic of Ireland find themselves rooted to the bottom of Group C, yet Trapattoni insists all is not lost.
He said: "We have to believe. Every game in this Euro could be a surprise. We have to believe this."