Despite initially appearing to be in control, United fell behind in the 28th minute as Aaron Mooy broke the deadlock shortly after Phil Jones' forced withdrawal with an injury.
His replacement Victor Lindelof was then guilty of a massive error for the second goal, letting Jonas Lossl's long ball go over his head and Laurent Depoitre duly punished him.
And Herrera was left criticising United's "passion", adamant that Huddersfield showed more desire.
"It's a very tough day, because we had a big chance to keep winning games and we didn't do it," Herrera told MUTV.
"They were more aggressive in the first half, played with more passion than us in the first 30, 35 minutes.
"After that we came back into the game better, but when you're losing 2-0 against such a passionate team, it is not easy to equal the game.
"Everyone has to analyse for himself what happened in the first half. When you play against a team that normally you are better than, you have to match their aggression and passion.
"We didn't do that. It cannot happen again."
Herrera's comments mirror those of his manager Jose Mourinho, who pointed out that Huddersfield had "the game of their lives" on Saturday.