Ireland currently sit fourth in Group C, level on points with Austria and three points behind Sweden in a three-horse race to claim second place behind runaway group leaders Germany.
Trapattoni had initially targeted four points from the two matches on this current international break, but a loss to Sweden on Friday has left Ireland needing a win tomorrow night.
"I have said to the players, we must play for our shirt, for our country and that what you have done until now was not a dream," Trapattoni told PA. "In the first half against Sweden I saw a very good team, and our attitude, our balance, our mentality is this. In the second half, we lost our enthusiasm.
"But yesterday I saw again a team with enthusiasm with our capacity, our strength, and I think tomorrow we can do well, as in the past. We are aware it's very important for both teams. We know the only objective is to win.
"Only with this result can we keep our hopes alive, but we still have three matches to play and anything can happen. What happened to us over 90 minutes against Sweden can happen to other teams. Anything can happen."
Ireland will also be hoping for Sweden slip up in their match against Kazakhstan tomorrow.