Goals from Mario Mandzukic, Thomas Muller and Arjen Robben secured a 3-1 win on the night for Pep Guardiola's side, who recovered from going behind to a stunning Patrice Evra strike to dump United out of Europe.
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He told Sky Sports: "It's not good enough. We've said that over the last few weeks. This club should be in the Champions League.
"It was always going to be tough tonight, we knew that, but the reason we're not going to be in the Champions League is our league form throughout the season. We take responsibility for that, we've had too many bad results and ultimately we've paid for that.
"We pick ourselves up, we finish the season as well as we can and we start again next year, believing we can challenge for the title again. That's all that matters now.
"This [the Champions League] is where we want to be, this where we've been for a long time and this is where we'll be back, I'm sure, in the not too distant future."