Phil Jones' late header proved to be a mere consolation as goals from Marco Streller and Alexander Frei sent the Swiss side into the knockout stages at the Reds' expense.
United instead face Europa League football for the first time next year which will present a fresh challenge as it remains a trophy the English champions have never won. Nevertheless, the necessary changes to the fixture schedule presents its own problems for the boss.
"Of course we're disappointed," Sir Alex stated. "There's no other way you can feel.
"We had so much possession of the ball and so many really good opportunities in the last third of the field. Some of our play up to that point was very good but you have to say we let ourselves down with the finishing part.
"The Europa League is a competition I've never been in at United and it does mean one thing - Sundays right through. Thursdays and Sundays. That's got to be dealt with and it's not the best but that's our penalty for not qualifying tonight."