Already on a yellow card, Ramsey pulled back Oguzhan Ozyakup’s shirt in the dying minutes at the Ataturk Olympic Stadium and was subsequently shown the first red card of his club career by referee Milorad Mazic.
The midfielder will now miss next week’s return leg at the Emirates Stadium.
“Both yellow cards for Aaron Ramsey are unbelievable. When you see the fouls they have made today it’s not serious. Just not serious,” Wenger told ITV.
Besiktas forward Demba Ba proved a constant threat for the home side as the former Chelsea striker went close on numerous occasions, while substitute Alex Oxlade-Chamberlain saw a late effort tipped on to the post.
Wenger conceded it was a frantic game and both teams wasted chances to take a lead to North London. However, the Frenchman believes his side are capable of doing the job at home in order to secure their place in the group-stage draw.
He added: “It was a difficult game played at a frenetic pace from the first minute to the last. We could have won it but they had chances as well, in the first half alone. In the end we didn’t lose and hopefully we will make it at home.
Despite seeing Ramsey red-carded and Mikel Arteta walk off the pitch with a suspected ankle injury, Wenger took solace in a pleasing performance from summer signing Calum Chambers.
Wenger said: “I think he was once again very good tonight and very convincing in his performance. He coped with the pressure, won the challenges and played on a pitch that was not easy. He did very well.”