Ireland are fourth in Group C heading into matches against second-placed Austria and Sweden, who sit in third, with all three teams on 11 points.
It is the Swedes up first at the Aviva Stadium on Friday, and Trapattoni knows by the time they come home from a trip to Vienna four days later he will have a good idea of their qualifying fate.
"These two games for us will be very, very important. I have said to the players, we must have trust and believe in our possibilities," he said.
"We have four very, very important days, but we must believe. We are the same in the table. We could be ahead of Austria in second place.
"We are the same in the table and only with our mentality and attitude and belief can we achieve this.
"After the last game against Austria, I could have been angry, but in the dressing room I was not angry because I must give them trust and confidence.
"It was a silly mistake. I spoke with the players who lost the ball before we conceded the goal, but I have to give them confidence because with the young, you must give them trust and also advice."
Trapattoni has called Bristol City defender Greg Cunningham into his squad as cover with Stephen Kelly having withdrawn for family reasons and Marc Wilson struggling with an ankle problem.
Richard Dunne, Robbie Brady and Shane Long were spared training on Monday to rest some aching muscles and James McCarthy is yet to join the squad amid rumours of a move to Everton.