Arsenal needed only a draw to leapfrog London rivals Chelsea into fourth but goals Ruben Neves, Matt Doherty and Diogo Jota in the first-half set Wolves on their way to a 3-1 win.
Arsenal looked short of ideas but managed a consolation goal with 10 minutes remaining when Sokratis headed in Xhaka’s corner at the far post.
In his post-match press conference Unai Emery revealed that despite the loss he was pleased with how they reacted after his team talk.
"In the dressing room we spoke of how we needed to recover and be strong in our mind," Emery told reporters on Wednesday night. Score one goal was the first idea and after if we can take minutes we can continue in our plans. The second half is different but not enough."
Speaking to BBC Sport, saying: "We spoke in the dressing room at half-time and we tried to see it as a new match and in the second half we changed our performance and scored a goal. We can be frustrated but the Premier League is about being consistent over 38 matches.
"We knew before the match that it was going to be difficult because all season Wolverhampton are feeling strong, defensively they are a good team and offensively they have very fast players. Their organisation was very good and to break this was going to be difficult. In the first 25 minutes we started very well, controlled the possession but did not have many chances to score."
Arsenal became the latest of the division’s top-six clubs to taste defeat at Molineux, where Chelsea, Liverpool and Manchester United have also been beaten this season.