The Gunners arrived in Istanbul under a cloud after their shock home defeat by Aston Villa in their opening Premier League match, as well as their inactivity in the transfer market.
But second half goals from Kieran Gibbs, Aaron Ramsey and Oliver Giroud powered them to a much-needed win in Istanbul in what Wenger had described as "a massive" match.
Wenger told Sky Sports: "It was a good performance in a heated atmosphere.
"We controlled the match and after the disappointment of the weekend we're in a strong position now. It was vital to get off on the right foot and that's what we did.
"We could have been a little bit shaky after what happened on Saturday. So for us it was very important to start on the front foot. That was vital tonight for us and we did it well."
Despite drawing a blank in the opening half in Istanbul, Arsenal came out firing after the interval and dominated their lacklustre hosts.
It was a huge contrast to their match four days before, where Wenger and his team were roundly booed by their home supporters.
The Frenchman added: "This team has shown a lot of mental strength. I told you on Tuesday that you had forgotten that this team has lost only one game since March under very, very special circumstance.
"Of course ,the environment we faced was difficult but the only way to do it is to go out there and play football like you want to play. I believe we played in a very, very heated atmosphere against a good team, but we had a proactive attitude from the first minute on, and that was certainly was very important.
"We did not come in shaking, but came in resolute and determined and with a desire to take the game to them - and overall we were in control."
The win, though, came at a cost as defender Laurent Koscielny was forced off with a cut head following a high boot from Pierre Webo, which left the France international needing hospital treatment.
An unimpressed Wenger said: "Laurent Koscielny has opened very deeply the skull and we had to take him to hospital.
"I was not happy with the kick because I feel always that you can ease a bit off. Only the player in the end will know what he did. We are concerned because we had to send him to hospital to see if he has not broken a bone."