The points were already in the bag with Arsenal leading 4-0 after an hour at The Emirates when Polish goalkeeper Wojciech Szczesny rashly took out Burak Yilmaz in the area.
He looked mortified as he walked off the pitch for the second time in consecutive home Champions League proper matches, having also seen red in the first leg of the last-16 clash against Bayern Munich last season.
Arsenal have had five red cards in the last seven matches in the competition, including one in each leg of the final qualifying round against Besiktas earlier this season.
Aaron Ramsey was sent off in Turkey and Mathieu Debuchy in the second leg in north London.
New club skipper Mikel Arteta was also dismissed away to Napoli last season in the group stage.
While Szczesny's rush of blood had no impact on Wednesday's result, a 4-1 win which put Arsenal second in Group D behind Borussia Dortmund, it did cause the home side to lose their shape and allow Galatasaray to mount a late rally after Yilmaz had tucked away the penalty conceded by Szczesny.
Against better opposition, such losses of concentration often prove fatal, as Wenger well knows.
Szczesny will now be suspended when Arsenal take on Anderlecht in their next match, although substitute keeper David Ospina made some fine saves in the closing stages and looks an able deputy.
Wenger refused to criticise Szczesny, saying the keeper was the victim of a loss on concentration by his team mates who conceded possession carelessly in a dangerous area in the build-up to the move that saw him bring down Yilmaz.
"We lost a ball in our own half and after that there was a through ball, " he said. "I saw (Szczesny) coming out and I thought maybe he had read the situation well
"But he was a fraction late and that can happen. I think we were more guilty to lose the ball in our own half -- it can be dangerous and we didn't defend too well on that front."
While red cards are annoying, the sight of red distress flares being waved around by Galatasaray fans and hurled on to the pitch -- temporarily holding up play in the first half -- was a worrying sight at The Emirates.
A club offical said seats had been damaged and that there had been some arrests of Galatasaray fans as police moved in.
There were also reports of a disturbance in a pub outside the ground where Galatasaray fans threw flares.
Arsenal could even find themselves in trouble with UEFA, despite the disturbance being caused by Galatasaray's fans.
