Vicente Del Bosque's men are overwhelming favourites to secure their first victory of the Group C campaign at the PGE Arena in Gdansk, with Ireland knowing they are facing a swift exit if they do not take something from an intensely difficult encounter.
However, the 73-year-old Italian is refusing to give up on his dream of reaching the last eight. "I am proud to be the manager of the Irish players because the Irish players have heart," said Trapattoni. "But we have achieved results not only with heart because we have met France, Bulgaria, Italy, many other teams and we played the same. We play our football.
"It's creative enough and it's technical enough," he said. "Maybe Spain have one or two more creative players, but football is not only about creative players. Today, football is about balance on the pitch and strength with attitude and also luck. We have attitude, mentality, commitment, technical ability. We don't make bets, but I think we can win. Why not?"
Even a point tomorrow night would leave the Republic in with a chance of making it out of the group if they could beat Trapattoni's native Italy in their final game. But while fans consider the various permutations, the manager is concentrating only on what lies immediately ahead.
He said: "We can hope. We have a very delicate situation now. We are playing against a very strong team but if we win tomorrow, we can have another attitude. Italy and Spain after the first game each have one point. At this moment, it's all open. Only after tomorrow can we say if we have an opportunity or not."
Ireland go into the game effectively with nothing to lose, but while Trapattoni acknowledges the difficulty of the task that lies ahead, he will not abandon his principles. He has hinted that there may be subtle change - he broke with tradition this afternoon when he declined to name his team at the pre-match press conference as he usually does - and it would be no surprise if the Republic lined up in a 4-5-1 formation in an effort to better limit Spain's all-star midfield.
Trapattoni said: "I can't give you the line-up because as I have said to you, I have to think very well about it. I will watch the [friendly] game, China v Spain, again. I have an idea, but we can't always give our opponents the line-up when we don't know theirs.
"Having nothing to lose does not mean we are not aware of the capabilities of our opponents," he went on. "When I first came to Ireland, I said if having nothing to lose means everyone just pouring forward gung-ho, all-out attack and conceding five goals, that means you are not really aware of the fact of who you are playing.
"A coach needs to be aware of how his own players play and their qualities," he said. "I have already said quite enough of this. We are going to play our own game in the knowledge of how good Spain are. To aim for the best result is the most important thing. If I can't play this football, I'm not going to give a present to a side like Spain. I'm not going to let them just take the ball and go up the other end and score a goal."