The Dutch giants dropped into UEFA's secondary competition after losing a two-legged Champions League playoff at the start of the campaign, going down 5-2 on aggregate to Rostov.
Ahead of next Wednesday's final between the two sides at the Friends Arena in Stockholm, Mourinho has added to the growing war of words with opposite number Peter Bosz by claiming that his team are lucky to have been given a second chance.
"They are a Champions League team, they come from the Champions League," he told reporters. "I always disagree with it. I don't think a team should play two European competitions in a season.
"If you don't qualify [for the Champions League] I think they should go home. We finish fifth [in the Premier League] last year. We went into the Europa League. We started the Europa League from beginning of season and we have to fight to get where we are."
Bosz has previously taken a couple of swipes at Mourinho, telling the United boss to stop complaining about supposed fatigue.