After a 1-1 draw in the quarter-final first leg last week, United took the lead at the Allianz Arena thanks to Patrice Evra’s stunning strike in the 57th minute.
My focus is getting a side together that gets us back into the Champions League
But Mario Mandzukic nodded in a equaliser moments later before Thomas Muller’s scuffed finish put Bayern ahead.
Arjen Robben then wrapped up the 4-2 aggregate win with a fine solo goal in the 76th minute.
“We’ve not got Champions League football [next season] which is disappointing but the focus now is that we get a team ready to get back in there,” said Moyes, whose United side are seventh in the table and seven points behind fourth-placed Arsenal.
“It’s a great competition, we’ve really enjoyed it and we need to get back in it.
“My focus is getting a side together that gets us back into the Champions League.”
Moyes felt that conceding so soon after taking the lead swung the tie back into Bayern’s favour.
“It probably went wrong 30 seconds after we scored,” Moyes continued.
“If you’re a schoolboy you’re told don’t concede after you score. From the kick-off they went up the pitch and scored, we needed five or 10 minutes to compose ourselves.
“The players didn’t do an awful lot wrong tonight. They played really well but it was just a couple of small errors that cost us in the end.”
“I think we had a great chance at 2-1, the third goal comes from two deflections. I never thought we were out of the game and I thought we had a chance, I thought there was a bit of bad luck in the third goal.”
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