A goal to Phil Jones midway through the second half spelled defeat for the Ukrainian visitors and also the end of their UEFA Champions League campaign - with their third-place finish in Group A putting them into the final stages of the UEFA Europa League.
Lucescu said his men performed admirably in the first half, but errors allowed a struggling United outfit to earn all three points to comfortably top the group from Bayer Leverkusen.
"We played very well in the first half - Manchester United only created opportunities after we made mistakes," Lucescu said.
"We had four or five good chances, and I think if we could have opened the scoring, the game would have gone another way.
"In the second half we weren't so energetic and you could see the difference between the Ukrainian and English leagues, as United play matches like this twice a week.
"That may explain their dominance after the break."
Lucescu rued results from earlier in the phase for Shahktar's failure to progress to the knockout stages.
"We should have secured qualification for the round of 16 in our home matches against United and Bayer 04 Leverkusen," he said.
"We had the advantage, but we were very unlucky."
Lucescu said it was too early to discuss their chances in the UEFA Europa League.
"It's difficult to talk right now about our prospects in the UEFA Europa League, because there are a lot of strong teams in the competition," he said.
"The first games after the winter break will have a big impact (on how we do).
"The newcomers are yet to reach the level of the players who have been here two or three years.
"Unfortunately we saw that in the second half today.
"Bernard and Fred haven't built up their strength yet, they are not yet ready for this level of match."
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