The hosts looked on course for a valuable three points in Group C thanks to Jon Walters' double, but David Alaba levelled with a deflected long-range effort in injury time.
Trapattoni said: "Think how disappointed the players are. We must give them morale and belief and support. We must be positive.
"We have three or four young players and some players who were playing only their second or third game.
"We must believe. I said yesterday we believe in this new revolution. We have to allow these young players to grow in confidence - why not?
"With more experience, we could have wasted some time with 90 minutes gone, but the draw is right because Austria played well."
Former Reading boss Brian McDermott has been linked with the Italian's position in recent days but the 74-year-old was defiant when asked if he would still be in the job in June.
He said: "Why not? We are in the table. It has not changed. We are the same in the table as Sweden, the situation has not changed."
Austria coach Marcel Koller said: "It's special in that the last goal was scored so close to the finish of the match and it was a well-deserved goal.
"We do take one point home, but we are still close together with the other teams in the table, so there's absolutely no reason for euphoria. We aren't through yet."