Doyle, top scorer for relegation-threatened Wolves this season, damaged medial knee ligaments 15 minutes into the victory that put Ireland level with Slovakia and Russia at the top of Group B.
Trapattoni, though, was hopeful he would not miss any competitive internationals.
"I think he will need one or two months. I hope he can come back for Macedonia away in June," the Italian told a news conference.
Trapattoni said he had little else to complain about.
"I have total reason to be very, very happy," he added. "We showed great personality at times and this shows the team has grown in self-belief and self-confidence."
Trapattoni saluted goalkeeper Kieran Westwood and defenders Kevin Foley and Darren O'Dea after injuries forced the coach to hand the trio competitive debuts.
However, he saved most praise for Spartak Moscow winger Aiden McGeady who ended a 38-cap wait for an international goal.
"He was the best player on the pitch," said Trapattoni. "He has improved his performance and personality.
"He is very self-confident and I think maybe a year ago he wouldn't have taken that shot at goal.
"We have players who have extraordinary potential but they are not aware of their potential yet," Trapattoni said, adding that Manchester United midfielder Darron Gibson belonged in that category.
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