Trapattoni's men require a positive result to keep their hopes alive of qualifying from Group C for the 2014 World Cup in Brazil ahead of Sweden and Austria.
Ireland go into the match full of confidence following the 2-0 victory over Poland last month in a friendly at the Aviva Stadium.
But the 74-year-old reckons Ireland will be playing to their own strengths in Stockholm rather than worrying about Sweden's talisman.
Trapattoni said: "Zlatan is Zlatan, but I am very confident in our players.
"I have seen their confidence this morning, and you just have to look at the game against Poland because the balance and the commitment and the technical ability that they showed, all of that makes me very, very confident."
And asked if he would attempt to man-mark the Paris St Germain star, Trapattoni said: "Not at this moment, I don't think so.
"I know how he is playing at the moment for his club, but I have to think about our balance and how our strikers can put them under pressure too."