United appeared to be in control until the 25th minute when Phil Jones was forced off with an injury, and Victor Lindelof replaced him in what proved to be a crucial moment in the match.
Aaron Mooy put the Terriers ahead three minutes later and Laurent Depoitre made it 2-0 shortly after that, punishing a woeful Lindelof error, as the Swede let Jonas Lossl's long ball go over him.
Marcus Rashford pulled one back 12 minutes from the end, but it was not enough to save United, who Mourinho does not believe would have deserved a point even if they had salvaged something at the end.
"I was not expecting that [poor first half]," Mourinho told Sky Sports. "The team that started with intensity, the team playing the game of their lives, won.
"Maybe in [the] second half we had more control, playing against a team and incredible wind. If we wanted a bit more then maybe we get a draw, but we deserve the defeat.
"We deserved it - the team that wanted it more, wanted to compete, to be more aggressive, won. When the best team wins, there is nothing to say.
"I am disappointed, but the reality is they were stronger than us. I prefer to be in peace with football and to be in peace is when the best team wins.
"It would be unfair if I point at the players involved in individual mistakes. I would if it was in the context of a great team, but it was in the context of what we were like in the first half.
"A bad team deserves a bad result."