The Republic of Ireland manager feels that his side put in a good display in their scoreless draw at the Cardiff City Stadium, and easily could have won the game
The Boys in Green had a number of chances to break the deadlock at the Cardiff City Stadium, but were denied the breakthrough goal by Welsh goalkeeper Boaz Myhill.
"We deserved to win because we had three or four great opportunities," Trapattoni told reporters after the game. "Their goalkeeper was fantastic. I was worried after the holidays that maybe the team did not have the same mentality, but I saw enough that was good."
"It was important to keep up our run of good results against a team like Wales which is good. Okay, they were missing [Gareth] Bale but they have other good players and it was important for us to start the new season without being beaten now when we are thinking already about the games against Sweden and Austria."
Ireland's next match is a home game against the Swedes on September 6, who put in an excellent performance to defeat Norway 4-2 on Wednesday night, with captain Ibrahimovic scoring a hat-trick. However, Trapattoni believes that his defenders can deal with any threat the striker has to offer.
"[Ibrahimovic] can score goals but we are a team with good organisation and that is our strength," Trapattoni said. "Ciaran Clark is strong, John O'Shea too.
"He's a good striker, and we know that he can score goals but he is only one player. What's important for us is the team. We need to keep a good order on the pitch, to be well organised and balanced; that is our strength. We have that now, the players know to do what I ask of them; that when the other team has the ball we must all defend."
Trapattoni knows Ireland must get a result against Sweden to stand any chance of progressing to the 2014 World Cup, and is hoping his squad can stay fit for the crucial qualifier.
"We must hope that we have no more injuries, though, because we need to have our best players for that game," Trapattoni admitted.