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.
Trapattoni said: "I am proud to be the manager of the Irish players because the Irish players have heart.
"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. Maybe Spain have one or two more creative players, but football is not only about creative players.
"Today [Thursday], 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?"
He said: "We have to believe in our quality, our attitude, our performance.
"Obviously, the last game, when any team concedes a goal after two minutes, it's very difficult to change the tactical situation.
"We will play to win, but we know also it is difficult because we know Spain are the world champions and they have very important players.
"In football, over 10 months, a strong team will win, but in 90 minutes, anything is possible."
He said: "I think psychologically, we have overcome the defeat against Croatia. We are back to believing in ourselves and our quality.
"Spain is a team with a lot of good technical players, we know, and it will be very important not to give them much space, particularly in midfield.
"They are very good at passing, they play the ball very fast and I have to think about the best solution for us for this game.
"Our objective is to be offensive and try to win the game, but at the same time, we need also to find a way to help the midfield because sometimes, we have suffered in this situation."
Even a point on Thursday 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 [Thursday], 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.
"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.
"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."
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Del Bosque sprang something of a surprise himself on Sunday evening when he started without a recognised striker, although his opposite number on Thursday is not expecting that to be repeated.
Trapattoni said: "I think Del Bosque will play with Llorente or Torres. The first game was a very important 90 minutes and I think Del Bosque knew how to approach the game against Italy.
"It was a very technical game and Del Bosque was hoping to rely on the quality of players such as Iniesta, Xavi, Silva and Busquets.
"But he could see that Torres was missing, so he changed it to get a striker up there. I think in the second game, Del Bosque will play a striker."
As ever, Trapattoni has studied tonight's [Thursday] opponents in great depth and was planning to watch again their recent friendly victory over China in the search for something that could prove crucial.
He said: "You learn something every day in life. You have to look at the small details which really determine the way games go and how goals go in.
"Once goals go in, that's how games change tactically and psychologically. I have been looking at DVDs now for more than 30 years and in every game, I see small details which have proved to be key to the way a game turns out.
"I always say coaches can't do miracles. Only players can do miracles.
"It's important that the coach knows every little situation."