They have now leapfrogged the Welsh and sit behind second-placed Russia, with Germany top and clear favourites to take the one automatic qualification spot for South Africa 2010.
But the 33-year-old insists that Finland have ambitions of their own far beyond just putting an end to Wales' dreams.
He said: "We wanted to qualify ourselves, and we still believe we can. It wasn't a case of stopping Wales qualifying because we believe that we can get out of this group and go to South Africa.
"We went close to qualifying for the European Championships, so we have always felt that we can win games like this.
"In fact I did not have much to do. We played extremely well and the defence were excellent and not much did come my way.
"We kept possession well and this was the best away game we have had for a very long time.
"Why should people be surprised that we could win this one? Our previous results have been good and we did very well away to Portugal in our previous match as a warm-up for this.
"And in our last qualifying group we had Portugal and Serbia and did very well. We were more than capable of beating Wales."
He added: "We have some very experienced players, Sami (Hyypia) was outstanding again, and in midfield we have Jari (Litmanen) who is very good on the ball and just seems to go on forever.
"Wales have much younger players, but they are stars who are coming through. Some of them did very well in the recent under-21s championship and they are stars of the future."
Finland's Birmingham-born boss Stuart Baxter hailed his side's victory, and the performance of veteran midfielder Litmanen, the former Ajax and Liverpool playmaker.
Baxter said: "Jari was outstanding, he is in the process of re-inventing himself at 38. He may not be able to do the runs he used to a few years ago, but he can still pass the ball and he dominated the game.
"He is an amazing person. He has been a great servant to Finnish football, a great player. Maybe people thought he would be coming to the end (of his career), but he had been working hard to be fit for this match because his Finnish club were out of season.
"He trained on his own for some while and did a lot of work to be fit for this one."
World Cup Group 4 Win Outright: Finland 33/1