The England striker, who sustained a toe injury last week, was passed fit to take his place in United's starting XI, but could not prevent the Red Devils from exiting the competition at the Allianz Arena.
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"I felt at times tonight he was having a struggle striking the ball but he's such a vital player for us," Moyes told reporters. "I never thought we were out of the game, I always thought we were in with a chance.
"When it was 2-1 we needed to score one more to get us to 2-2, but obviously that didn't go for us. I thought it was a bit of bad luck in that third goal.”
Manchester United were ahead for just 73 seconds before Bayern’s equaliser, and despite the Scot being pleased with the overall performance of his players, he bemoaned his side’s lack of focus from the re-start.
“If you lose a goal right after you score it makes the job really difficult. If you're a schoolboy you get told once you score make sure you don't conceded right away and we conceded too quickly," he said.
"I don't know if it was a bit of concentration after we got the goal but we had enough experience on the pitch tonight.”
United have been in each of the last 18 seasons of the Champions League, but this run would now appear at an end, with the side seven points adrift of fourth in the Premier League with five games remaining.