The Gunners' boss has come in for criticism following failure to strengthen the squad over the summer - problems which were exacerbated by the 3-1 home defeat on the opening day of the new Barclays Premier League season to Aston Villa, when England midfielder Alex Oxlade-Chamberlain suffered a knee injury which could sideline him for up to three months.
Wenger, though, had continued to champion the mental strength of his current squad - and was proved right as they came through the white-hot atmosphere of the Sukru Saracoglu Stadium with second-half goals from Gibbs, Aaron Ramsey and Olivier Giroud.
Full-back Gibbs, who played despite a head wound picked up against Villa, revealed there was a sense of determination within the group to show their manager's continued faith was justified.
"The performance was needed after the start of the season and to prove to ourselves and everyone what we are capable of," Gibbs said.
"He (the manager) believes in us and we believe in him, so we felt we had a point to prove to him and the fans.
"We have done that and now it is just about getting on with this season and we are determined to get results like we did in Istanbul."
Gibbs continued: "We wanted to do it for our fans more than anything and put last week's disappointment behind us.
"I think we have done that now and we have to just focus on the weekend and make sure we are strong for that now."
It is, of course, not the first time Wenger's resolve has been questioned, as his side swam against a stream of negativity last season to win eight of their final 10 league matches after bowing out of Europe with a morale-boosting victory over eventual champions Bayern Munich in Germany.
Gibbs is in no doubt the team can continue to answer all questions thrown their way.
"We have dealt with the pressure of the past couple of seasons - stages like this, last season before the Bayern game and after the Milan away game - and the players stepped up and showed what they are made of," he said.
"Winning in Istanbul showed what we are looking to produce this season."
- Sports & Recreation
- Barclays Premier League