The Republic of Ireland boss praised his team's performance against Erik Hamren's side and believes that they can continue to build upon it as the group progresses
The Italian tactician spoke in positive terms about the performance and indicated that the players could take confidence from the manner in which they approached the game against Erik Hamren's side, away from home.
"We started very well in the first few minutes," Trapattoni said in the post-match press conference. "After that the game was evenly balanced I think. I don't know if Sweden was afraid of us but we were not afraid of them."
He continued: "It was very, very important for us not to concede a goal because until now we have played many games without losing an away game but we achieved that and we are satisfied.
"But we played well against Poland and all of our young players will take confidence from this game and improve more in the future as a result. I think in the future this can become a great team.
Trapattoni also praised his goalkeeper, David Forde, after the Millwall shot-stopper made a number of crucial saves during the game.
He said: "I think after this we can take more confidence, be more technical and play better football. And our goalkeeper, others were injured and we chose (David) Forde. I have particular respect for Forde, he played well tonight and I congratulate him on his performance."
"Any manager would take confidence from a result like this," continued Trapattoni. "We have to believe before every 90 minutes that we can do well and this performance will help but we also have to have respect for the opponents.
He added: "I know these (Swedish) players, they play very well for their clubs and it will be difficult when we play them again.
"Austria too are good; I know, I worked there and I know their players well but this is an important result for us and a good performance and now, next week, we have a big opportunity to take another step towards the qualification position."
The Republic of Ireland will continue their World Cup qualification campaign on Tuesday, March 26, when they face Austria at the Aviva Stadium.