The Ivory Coast front man - who left Chelsea after spearheading their 2012 Champions League final victory before a short stint with Shanghai Shenhua in China - converted a soft penalty on 78 minutes before then producing a crisp finish as the Turks secured their second victory of the weekend tournament, having fallen behind to Theo Walcott's first-half curling effort.
Arsenal showed good form in patches, but once again had no answer to the 35-year-old, who had been on Wenger's radar when a youngster at Guingamp.
So far, France Under-21 forward Yaya Sanogo, a free transfer from Auxerre who was handed a start in attack today, remains the Gunners' only summer purchase, despite having a sizeable kitty with which to strengthen a squad that has not delivered a trophy for almost a decade.
Arsenal are expected to increase their £40million + £1 bid, which they believed would trigger the Uruguay forward's release clause, although Liverpool remain adamant they will not sell - with manager Brendan Rodgers yesterday suggesting £100m Real Madrid target Gareth Bale could not be "valued at more than 100% more than Luis Suarez."
Wenger, though, insists his club will continue their negotiations away from a public auction.
He said: "We try to do it properly, but a transfer is always an agreement between three parties and we have always done that until now."
Wenger admitted he would have preferred to get his transfer business done ahead of the crucial Champions League qualifier at the end of the month, but does not intend to let that alter his intentions.
"Let's count first on what is here and if we can add something, we will do, but it is very difficult to predict if something will be sorted out before we play in the Champions League qualifier," he said.
"I think we have enough quality to achieve it with the players we have in at the moment and if we can have some more in before then, it's even better."
Wenger continued: "We just want to be ready. What is important for us is we have only 90 minutes now before we start the (Premier League) championship, it is important we recover a bit from the good days and we prepare properly for our next game which is against Manchester City in Helsinki, and then that we start strongly in the championship because that will have an influence on our performance in the Champions League.
"It is difficult, a stressful situation, but we did fight very hard to be in that situation and now it's time to take advantage of the fact we finished fourth and we have an opportunity to qualify. Of course it's always very tricky to qualify, but we have the experience of having done it before."
Arsenal look set to offload both Ivory Coast forward Gervinho and Morocco striker Marouane Chamakh. Wenger confirmed: "Gervinho is on a good way to Roma, and Chamakh on a good way to Crystal Palace."
Former Gunners captain Cesc Fabregas, meanwhile, is a reported target for Manchester United, with Barcelona manager Gerardo Martino claiming it would be up to the Spain international where he played next season.
Arsenal are understood to have first option on Fabregas, who returned to his boyhood club in the summer of 2011, but Wenger feels his former talisman will remain at the Nou Camp.
"What I know is Fabregas will stay one more year at least in Barcelona. That's the information I have. If that changes, I don't know, but that is what I have been told," Wenger said.
Arsenal had battled back from trailing 2-0 against Rafa Benitez's Napoli at half-time yesterday to draw, but could not hold out against the Turks this afternoon, as the second-half introductions of Drogba and Holland forward Wesley Sneijder proved decisive.
"We were in control, they didn't look dangerous, but we were not capable of maintaining physically that rhythm and control in the second half and we were punished for it," said Wenger. "We were exhausted in the end, but it was a good preparation."
Wenger felt Sanogo's performance was sound, the young French forward having shot straight at goal with an early opportunity which proved his best chance.
"Considering he has only just come back from holiday with only three or four days' training, what he did do is encouraging," said the Arsenal boss.