The Irish headed to Poland on the back of a 14-match unbeaten run but their European Championship campaign ended in failure as they lost all three of their matches and scored just one goal.
The poor performances led some to question Trapattoni's place at the head of the team, and his leadership suffered another blow last week when it emerged that Darron Gibson had rejected a call-up for this Friday's World Cup qualifier in Kazakhstan - a game he would have probably started in light of an injury to midfielder Paul Green and the suspension of Keith Andrews.
Yet Tardelli, who has been in Trappatoni's backroom staff ever since the 73-year-old took over in 2008, thinks the Ireland head coach is as determined as ever to prove his doubters wrong.
"Giovanni wants to work always every day. He is full of enthusiasm, just like he was the first time I met him," Tardelli said. "I don't understand why Giovanni is (being criticised).. because he achieved good results."
"I know he has said he has retired, but I hope he will be back for the Germany (qualifier in October). It is possible," Tardelli said. "I don't know if he will or not, but I always see him during Fulham's matches and I think it is possible, why not? He is a very good player. He said he has stopped but I hope he will come back."
Questions have been asked whether Gibson, who has impressed since moving to Everton, will make himself available for Ireland while Trapattoni is in charge, but Marc Wilson is sure the midfielder will not prolong his exile from the international scene.
"I know Darron quite well. I think he will be back again," Wilson said. "I hope he does because he is a good player and I think he could be really good for the team.
"I could see why he would be disappointed (that he didn't play at Euro 2012). He is a good player, but the manager selects the team and you have to respect his decision and just get on with it."