The 22-year-old recently secured a lucrative move to Everton from Championship side Wigan Athletic and Tardelli has challenged the midfielder to show his worth
The new recruit is expected pick up his 17th cap in midfield for the Boys in Green against Sweden on Friday and Tardelli had a strong message for the young midfielder.
"He must show that he's a good player," Tardelli told reporters in Dublin. "Something must change in his mind. Now he's in a different team, an Everton team that wants to win."
Tardelli confirmed that Anthony Pilkington was fit, but did not reveal if the player was expected to start on Friday. The Norwich City winger trained separately in the gym at the request of his club Norwich City after a light individual session and could be in line to make his debut in the absence of Aiden McGeady.
"Pilkington hasn't a problem. He's following his club training programme," Tardelli told reporters. "It's tough to decide on the players, because all the players are very fit. We have good options for Sweden."
There was, perhaps, no surprise that Tardelli gave little away in his after-session update in terms of the identity of those who will start on Friday but the usual training match hinted at the possibility of Cox being given the nod while Paul McShane also donned a bib in the game.
"Simon Cox is a good player, he can play left, right and striker," said Tardelli. "But I don't know if he'll play against Sweden."
Elsewhere, there is healthy competition for places in the centre of defence, with Queens Park Rangers defender Richard Dunne in line to make a return to competitive international football.
"I think so, but we have many options," Tardelli said of Dunne's potential involvement against Sweden and Austria. "He can play two matches. Richard is important for us. He's very strong physically."
Giovanni Trapattoni will name his starting XI on Thursday September 5 ahead of the squad’s final training session which will take place at the Aviva Stadium.