This was exactly what Chelsea, last year's Champions League winners, did as they beat Benfica to lift this season's second-tier European club competition in Amsterdam on Thursday night.
Arsenal and Chelsea had initially started the 2012/2013 campaign in the Champions League, but could not get through in the top two places - Chelsea becoming the first holders unable to make the knockout phase.
Wenger, whose Arsenal side are bidding to qualify for the Champions League group stages for the 16th consecutive season, feels the system needs to be reviewed.
"You have two teams in the final who were in the Champions League, their target at the start of the season was the Champions League, not to win the Europa League," said Wenger.
"We raised that question many times at UEFA: is it right to reward teams basically for failure?
"Every year now, in the Europa League, you have two teams who have been not failures, but who have been (first) in the Champions League.
"The teams who go through in the Champions League to the last 16 don't have a chance after.
"If you go out in the last 16 (of the Champions League), you don't drop into the Europa League.
"If you don't qualify (from the group stage), you have a chance of winning the Europa League.
"If I had won the Europa League like Chelsea I would have been happy as well.
"It is a trophy, but, overall, it raises the question."
Wenger feels the integrity of the Europa League would be raised if sides from the Champions League were not allowed a second chance of success.
"You can say that many teams who start the Europa League fight together, then, in the middle of the competition, some come in and suddenly they are all potential winners, but they didn't start the competition, they were in another competition," the Gunners boss said.
"For the rest, congratulations to Chelsea.
"It looks even more fantastic because they have won the Champions League and the Europa League in two seasons, but usually that cannot happen."