The Gunners, who are aiming to reach the Champions League group stages for a 17th consecutive season, toiled for long periods in the first half at the Ataturk Olympic Stadium but went desperately close as Alex Oxlade-Chamberlain hit the post in the closing stages.
Wenger's side will now need to get the job done at the Emirates next week, when they are expected to have German World Cup-winning trio Mesut Ozil, Per Mertesacker and Lukas Podolski back, but they will have to do it without talisman Ramsey.
The 23-year-old Welshman picked up his second yellow for pulling back former Gunners midfielder Oguzhan Ozyakup, but Wenger felt referee Milorad Mazic, who also received criticism for some of his performances at the World Cup, made a strange decision.
"It's not serious to get the second yellow card when you see the kind of fouls they have made today," Wenger told Sky Sports.
Although he was annoyed about Saturday's matchwinner against Crystal Palace being dismissed, Wenger acknowledged the part played by Slaven Bilic's well-drilled outfit.
"It was a difficult game, played at a good pace, a frenetic pace, from the first to the last minute and we could have won it," he added.
"We had chances to win the game, but we couldn't do it.
"They had chances as well in the first half especially, but in the end we didn't lose the game and hopefully we'll make it at home."
Another potential headache for the Arsenal boss ahead of that second leg could be Mikel Arteta after the Spaniard went off after 50 minutes with an apparent ankle injury.
But Wenger still insisted that the Gunners are the ones in the driving seat.
"Our target is to play better every game," Wenger added.
"Technically we can do better, and will aim to do so in the next game."
The return leg at the Emirates is live on Sky Sports 5 HD next Wednesday, with coverage underway from 7pm.