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."
The victory was, though, not without cost as centre-half Laurent Koscielny had to be taken to hospital after suffering a cut head when he received a high boot from Fenerbahce striker Pierre Webo.
The France international was able to return to England with the rest of the squad last night, but it remains to be seen whether he will be fit for Saturday's lunchtime visit to Fulham.
With captain Thomas Vermaelen still sidelined by a back problem, Wenger could be faced with something of a selection dilemma at the centre of defence.
However, Bacary Sagna did play there during pre-season and, with Spain full-back Nacho Monreal available again after his own back injury, could be moved across to the centre at Craven Cottage.
Wenger, meanwhile, may have ruled out going back in for Liverpool striker Luis Suarez, but the Arsenal manager revealed he expects the stakes in transfer "poker" to be upped over the closing 10 days of the window.
Newcastle midfielder Yohan Cabaye and Real Madrid's Karim Benzema are both reported targets as Wenger looks to dip into the £70million Emirates Stadium warchest ahead of the September 2 deadline.
Wenger later revealed he expected Koscielny was not set for a lengthy spell on the sidelines, but the defender will not feature at Fulham because of his red card against Villa last weekend.
Speaking to the club's official website, www.arsenal.com, Wenger said: "He's like a boxer who had a hard fight the night before; lots of blood around his eye and a deep cut.
"He is suspended for Saturday anyway, but let's hope he recovers for next Tuesday [second leg against Fenerbahce].
"It will be short because the cut is very deep. Hopefully it will be all right."
Wenger gave an update on Vermaelen's recovery, which is going well.
"He is out running. He's on the pitches again, but there's still a good few weeks to go for him to get his fitness," the Arsenal boss said.
"We have Nacho back and Thomas soon back so that's all good news for us."