The 4-2 quarter-final aggregate loss all but confirmed the three-time winners of the competition would miss the tournament for the first time since the 1995-96 season next year.
With the odds well against United claiming fourth in the Premier League, they look set to face a wait before playing on Europe's biggest stage again.
"It's obviously not good enough," he told Sky Sports. "We've said that over the last couple of weeks. It's obviously not good enough because this club should be in the Champions League.
"It was always going to be tough tonight. The reason why we're not in the Champions League next season is not so much because of tonight or last week, it's about our league form, so we take responsibility for that.
"It's been over a long period of time that we've had bad results and ultimately we've paid for it.
"I don't think there will be a knock on effect. We need to pick ourselves up and finish the season as well as we can and we start again next year coming back believing we can challenge for the title again. That's all that matters now.
"This is where we want to be. This is where we've been for a long time and we'll be back here in the not too distant future."