Trapattoni's team have been in the spotlight for all the wrong reasons after their last appearance at Dublin's Aviva Stadium ended in a humiliating 6-1 defeat to Germany.
The Republic take on Greece on Wednesday night knowing nothing less than victory will appease the large section of the Irish public that have been calling for Trapattoni to be sacked since their winless Euro 2012 campaign.
However, McCarthy - who missed the tournament after his father was diagnosed with cancer - believes the Italian will prove his critics wrong.
"I think he's the right man," he said. "He has achieved so much for Ireland. The result against Germany wasn't acceptable, but I think he will kick us on again.
"He got us all up for the Faroe Islands game (a 4-1 win) and hopefully we can get back to back wins now.
McCarthy also defended Trapattoni's perceived reluctance to blood young players in his team, adding: "He will blend the kids in gradually. He won't just throw everyone in. He can't. That's not the right thing to do.
"His communication is fine. We all understand what we need to do and what we have to."