"I am not surprised because he is a player who has good timing with his runs and is a clinical finisher who can score goals," said Wenger, "but I always believed that he will be a fantastic player and I was never concerned.
"For me, most of all is that he continues to develop as a team player.
"What happened on Wednesday we have to consider to be an exception - even for players of 25, 26 to score three goals in an international game is a one-off."
Wenger added: "At the start of the season Theo had made a step forward and you could see that in training.
"Theo has become more of a man and more mature in his game, developed his link play, his first touch, his commitment - and there is still a lot to come from 19 to 23 years old."
Wenger believes Walcott can develop into a central striker, but for the moment is happy enough for the youngster to continue learning his trade on the flanks.
"He can play down the middle, but at the moment, I do not believe he is ready," said the Arsenal manager.
"He is still learning his job on the right or the left, sometimes through the middle - but block him against the line and then show us you can do it because that makes it easier for us in the middle."
Wenger observed: "Don't set any limitations on any human being because once you have talent the rest is down to how much you want it and to how intelligent you are.
"I believe he is hungry in a quiet way - quiet determination - and he is intelligent. You can be very optimistic. The rest is down to injury and being regularly at the top level."
Walcott was back in at Arsenal's London Colney training complex today following his return from Zagreb and Wenger has been impressed by the way the youngster handled himself after once again being thrust into the media spotlight.
"I haven't seen the game last night, but I listened to his interview after the game this morning and I was as pleased with his interview as with the three goals he scored," said Wenger.
"I am not sure if I had scored three goals in an international game I would have given the same interview. That shows he is a good analyser, clever, well balanced, feet on earth.
"Straight away after the game he analysed the consequences of what happened to him last night and how he has to deal with that.
"I feel that is more important for his career than the three goals he scored because that shows a great sign of intelligence and maturity."