Arsenal trailed 2-0 at Goodison Park with seven minutes remaining but rescued a point thanks to late strikes from Aaron Ramsey and Olivier Giroud.
The fighting response from Wenger's side added to a last-gasp win over Crystal Palace on the opening day and gave them a boost ahead of the second leg of their UEFA Champions League play-off on Wednesday.
Alex Oxlade-Chamberlain saw his strike come back off the post in the dying stages of last week's clash but in truth an Arsenal victory would have been unfair on their opponents, who impressed, with frontman Demba Ba a constant threat.
"It [Everton draw] makes us strong in our belief and that's an important quality for Wednesday night," Wenger told Arsenal's official website.
"This game was very physical – let's prepare well and then I believe we have a good chance.
"The task is clear. We want to win the game at home. It's the Champions League so it will be a thriller because [Besiktas] are a good side."
Giroud suffered a late ankle injury at Goodison Park and Mikel Arteta (ankle) and Yaya Sanogo (hamstring) are also in doubt, while Theo Walcott (knee) and Kieran Gibbs (hamstring) continue to sit on the sidelines for Arsenal.
First came a 5-2 aggregate win over Feyenoord in the Champions League's third qualifying round in which Ba netted a second-leg hat-trick.
