Despite revealing that Olivier Giroud will be out until the new year, Wenger was pleased to have progressed.
Chile striker Alexis Sanchez operated as a lone striker and claimed the vital goal which enabled Arsenal to progress into the group stages of European football's premier club competition for a 17th successive season on the stroke of half-time.
"Not qualifying is unthinkable until it happens, and then everyone thinks 'why did it happen'," Wenger told Sky Sports.
"It is a weight off our shoulders now because we can focus on the Premier League, wait for the draw.
"We played against a good team and had to show a good fighting spirit.
"We feel we have done the job and we have a clear conscience."
Arsenal had to finish the match with 10 men after Mathieu Debuchy was sent off for collecting a second yellow card - a decision that Wenger was not entirely comfortable with.
"I was very worried because you never know as we have some players on the edge physically," Wenger added.
"I thought it was very harsh because Debuchy played the ball and maybe with the anger from our side on the bench we saw he played the ball.
"The referee was on the other side."
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