Ireland sit fourth in qualification Group C and the best they can hope for now is a runners-up spot behind runaway leaders Germany and a place in the play-offs.
Trapattoni is convinced he can steer the Irish to Brazil, having helped to end their long way for tournament football at Euro 2012.
Ahead of Tuesday's crunch clash with Austria in Dublin on Tuesday, he said: "We must win, it is the only option.
"After Friday's performance and result (a 0-0 draw in Sweden), we can go into that game with more confidence than we had in recent games.
"We've rebuilt the team, remember. Nine of the men who started on Friday did not start in the Euros. Four of them - Marc Wilson, Seamus Coleman, James McCarthy and Ciaran Clark - weren't even in the squad.
"So we are coming again. In the past I got Ireland to the 2010 World Cup play-offs and then to the Euro finals. We can achieve this again."
Trapattoni was believed to be on borrowed time following a 6-1 mauling by Germany in October, but the vastly-experienced Italian tactician claims he does not feel pressure.
He added: "I am old, too experienced to worry about losing my job.
"Plus, the FAI had the nerve to back me. We had a few bad results. If this was a club side, it would be bye-bye but the FAI knew what we had achieved in the past and they stuck with it.
"They know that when you lose a game, it is not always your fault. You can miss a penalty or the goalkeeper can make a save. I'm very serene about my situation.
"What people say about me and how things are going is not important to me."