The Frenchman scored the only goal of the game at the Emirates Stadium to lead the Gunners to a 1-0 victory in the North London derby.
"It shows you that every striker who comes here improves," Wenger told Arsenal's official website. "We must have some quality to develop this aspect of the players.
"I don't fix him any limit but today (Sunday) he showed a good mixture of physical commitment and technical ability. That's what you want from a striker. That shows with us he has developed his technique and I think he had a real physical presence.
"Already last year when I was not completely happy with his performances sometimes, when you spoke to the managers of the other teams, they told me always that their defenders said that he's a handful. When you get these kinds of vibes, you always think there is something to work on."
Wenger went on to praise the rest of his players for their performance against Tottenham.
"We [were] backs against the wall and absolutely had to win after Villa and on top of that, [it was] a very intense derby having played very difficult games in the last two weeks," the Frenchman added.
"I thought before the game that if we had not made the difference, the last 20 minutes could be difficult. They were but we have shown another aspect of our team - commitment, resilience, desire to defend together and that was fantastic as well. It's quality that will be needed.
"What pleased me is that we have shown that resilience. What pleased me as well was that Giroud had an exceptional performance, looking like really scoring from game to game. Offensively [Theo] Walcott was dangerous and in midfield, the fact that [Mathieu] Flamini [came off the bench] for a first game and did very well. That is of course very positive for us."
Arsenal are currently fourth in the league table with six points from three matches.