Frenchman believes his team have matured after grinding out result
Arsenal threatened the Stoke goal on several occasions in the first few minutes of the game and grabbed the opener through Sebastien Squillaci, which turned out to be the only goal of the match.
Stoke came out in the second half a different team and began to break down Arsenal's play, but the north London side held on and got the three points, much to the delight of their manager.
Wenger said: "We did the job after the injury in a very professional way against a Stoke team who defended very well. They were very compact but we were intelligent, calm, patient and overall I believe we were resilient."
The Frenchman was all too aware of the throwing ability of Stoke's Rory Delap and light-heartedly commented on the danger posed by the long throw.
He continued: "I wonder whether we should change the rules a little bit. Because when they had a throw in at halfway they threw it into the box so every time you have to face a danger and it is very difficult to defend. We did it very well though and did not concede a goal.
"I am very proud of that because it is so difficult against Stoke. They can change games in fractions of minutes. It is a problem you face here at the Emirates but at Stoke, he [Delap] can throw it in from his own half, so you have to be prepared for it."
On whether Wenger had an issue with Stoke's style of play, Wenger said: "No. I have no issue with the long throws and I do not have issue with any other aspect of their game. It is a team you know you have to prepare mentally for before the game because you will not take the points if you do not do it.
"Nobody likes to play against Stoke because they have a very special way to play the game, but I have to say tonight for me they defended in a very intelligent way. When we found some space they quickly cut it off and we could not take advantage."
With the game being the sole fixture in the league on Wednesday night, Wenger was happy that his team took full advantage of being able to catch up with Manchester United and move away from the likes of Manchester City and Tottenham.
The former Monaco boss added: "Tonight was a night where nobody else played and if you can take advantage with three points and creep up and close the gap at the top it is a good night. If you can do that it shows you are hungry for success because with the number of games we have played recently, not to make a mistake was good. We lacked a bit in attack but you could feel the team did not want to make a mistake."
Wenger also believes that his team are now playing with the maturity that they have lacked in previous seasons.
He explained: "We have matured because we won a game when we were less fluid. We won with intelligence, our brains and calm and that is what has changed. One or two years ago when we were not on our top game we dropped points. Tonight we showed we would not make a mistake and I must give a lot of credit to our players for that."