The Italian opted to replace left-winger Aiden McGeady eight minutes into the second half of Sunday night's 3-1 reverse in Poznan.
But rather than turning to specialist McClean, who won rave reviews for his performances with Sunderland in the Premier League during the second half of last season, he asked striker Simon Cox to line up in the Spartak Moscow man's place.
Trapattoni had anticipated the question and was ready for it when it arrived at the Republic's Gdynia training base this evening.
He said: "I was waiting for this question. Remember when you asked me why five strikers? I said Cox is also a winger and he can also play in a three as an attacking striker. Remember when you said this?
"Cox is one of the strikers but also at his club, can play right or left. He is also a striker in fact and in the past, has scored goals.
"Our wingers yesterday were not too often in on goal. I ask you, how many goals has McGeady scored? How many goals has (Damien) Duff scored? They are our wingers.
"You don't remember? Also me. This is important because at that moment, we needed someone in that position who could also score.
"Remember also against Italy? Remember Cox scored from this position? He's a good player, Cox."
Whatever the merits of the 25-year-old West Brom striker, there is a genuine excitement in Ireland about McClean, the 23-year-old former Derry City midfielder who only made his senior debut for his country as a substitute in February.
Trapattoni decided to include him in his final 23 for Poland and Ukraine, but remains to be convinced that he has the experience to do what he does best under the glare of an entire continent.
The 73-year-old said with a smile: "You are friends with James, no?
"I have a duty. It would have been his first [competitive] game. When there are senior, experienced players in this situation, maybe there is tension. You can understand how much more tense a young player can be.
"It's important we give them a quiet opportunity, not when we need their performance under pressure. It's a heavy weight on his shoulders.
"McGeady is one of our best players, and Damien Duff the same. His time will come in the future."
Whether or not McClean can force his way into Trapattoni's thinking over the next few days remains to be seen, but what is plain is that the man who became the oldest manager to send a team into battle at a European Championship finals last night has work to do before Thursday's crucial clash with Spain.
Ireland must take something from the game in Gdansk if they are to keep alive their hopes of reaching the last eight, and they can start to pack their bags if the reigning champions, who drew 1-1 with Italy last night, emerge victorious.
Trapattoni said: "Spain are the World champions. They have 10 players playing for Real Madrid, 10 players playing for Barcelona - they are missing only (Lionel) Messi.
"We know their technique, we know their quality, we know. But over 90 minutes, it's not enough.
"I can also remind you of the Champions League final - Bayern against Chelsea. Bayern played 70 minutes and had 17 corners and one corner for Chelsea, and Chelsea won. Football is so.
"Obviously, Spain, it is a team with confidence, with trust. We know their quality, we know their self-confidence. We know this, and it will be important for us not to concede space to them because they play two-touch easily. They have good quality."
Trapattoni and his staff put their players through a light session this afternoon with central defender Richard Dunne sitting out, but only because of blisters, while midfielder Darron Gibson has undergone a scan on a tight thigh muscle, but does not have a lasting problem.
There was a sense of deflation among the Irish fans in Poznan as they reflected on a damaging defeat, but the manager was more measured after re-assessing a difficult 90 minutes.
Trapattoni said: "This morning, I watched our game with more calm and I have come to the conclusion that we played well enough, but not as well as Croatia.
"Obviously in terms of the performance, Croatia were superior to us. But our performance was more than positive."
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