An own-goal from former United defender Chester gave the visitors the lead in the 66th minute, and the eventual win, at the KC Stadium prompting words of praise from Moyes.
"We didn't start well, but all credit to the players for getting themselves back,” he told Sky Sports.
"I think it's what Manchester United are capable of, they have been over the years.
"We played well enough after that to score goals, and create goals. It was a bit harem scarem in the last five minutes but I'd have taken that after being 2-0 down at the start of the game.
"The boys showed great character to come back."
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