A stunning strike from Cristiano Ronaldo, his first for Juventus in the Champions League, had the Italian champions out in front in second half, only to see Juan Mata strike from a direct free kick before Ashley Young's delivery knocked in for an own-goal by Alex Sandro.
After the match Allegri was disappointed with the loss, believing that, rather than skill from Manchester United, it was his own team's poor decision making and sloppy finishing that eventually doomed them.
“It’s a disappointing defeat, because the team played well. We need to improve our finishing, because we never manage to finish games off when we’re in control," he told Football Italia.
“We knew with (Marouane) Fellaini on that we had to avoid giving away free-kicks, but we’re doing that too much this season, giving away a lot of free-kicks.
“The only way Manchester United were ever going to score was from set-pieces and we gave them the opportunities.
“Nonetheless, we are still top of the group. It’s understandable to have a win and a defeat to Manchester United, although probably not when you look at how the games actually went."
Despite the defeat, Juventus sit top of Group H, having picked up nine of 12 possible points, and Allegri believes the loss to United could prove beneficial for his side, even if they did fail to confirm their place in the last 16 on Wednesday.
“I think it’ll do us good in the long run, as we need to learn not to fall asleep in these situations. I saw Manchester United play the same way in the Premier League at the weekend, they did very little for 80 minutes and then won in very similar circumstances.
“We had the chance today to secure the top spot early. I compliment my team for a good performance, but a good performance without a result isn’t worth very much.