A mistake-riddled 3-1 defeat in their opening Group C match put a dampener on Ireland's first appearance at the finals since 1988 and means they must avoid defeat on Thursday against world champions Spain who drew 1-1 with Italy.
"It's important we recover psychologically and believe again because we have to remember how many games we had played without conceding a goal," the seasoned Italian, whose side had kept 11 clean sheets in a 14-match unbeaten run, said.
"We believe in our strength."
Since taking over four years ago Italian Trapattoni has transformed Ireland's fortunes and they were desperately unlucky to miss out on qualification for the 2010 World Cup finals.
Despite being placed in a tough Euro 2012 group that also includes four-times world champions Italy, hopes were high that Ireland could sneak into the quarter-finals but defeat against Croatia, a match that was targetted as the most likely victory, means the party could be cut short.
They never really got started against the lively Croatians, conceding a soft goal to Mario Mandzukic within three minutes.
Although Sean St Ledger equalised they were rocked either side of halftime with Nikica Jelavic's shot and Mandzukic's header which went in off keeper Shay Given sealing defeat.
FRESHEN UP
Ireland looked heavy-legged for long periods and lacking in creativity when chasing the game and Trapattoni hinted that he may freshen up the team for the clash with Spain in Gdansk.
Many of the travelling Irish fans frequenting the bars of Sopot, close by the team's training base on Poland's Baltic coast, want to see an injection of youth such as Sunderland's highly-rated midfielder James McClean.
Whether or not the wily Trapattoni will risk tinkering too much against Spain is doubtful although he did offer some encouragement for the fringe players.
"Spain is another game and then we have to think very, very much," the 73-year-old, who tasted only his third competitive defeat as Ireland boss and his first on the road, said.
"If I decide to change, it will not be because a player played badly or does not deserve to play. We have another game. Our opponent only drew and has only one point."
Defender Stephen Ward said they would be huge underdogs against the Spanish but hoped the luck of the Irish would return after two of Croatia's goals owed much to large slices of fortune.
"Against Spain we have nothing to lose so we have to go out and give it everything and hopefully we can get a bit of luck on Thursday and then go into the Italy game with a chance of qualifying," he said.
