The Foxes fell behind to an early goal from Adam Clayton and, although Michael Keane quickly replied, Sean Scannell got a second-half winner for the visitors.
Pearson said: "We were not good enough in both boxes. That is what cost us.
"We should have avoided giving away the free-kick for the first goal and were then caught on the counter-attack to concede the second.
"And we were not clinical enough in their penalty area, when we had our chances. We didn't secure the ball well enough but still had opportunities.
"There were some good passages of play and there was a good work ethic but we were let down, because the quality in both boxes was not what it has been.
"We are disappointed to be out of the FA Cup but I have got a lot of faith in this group of players.
"The league has always been our priority but I would still have preferred to go through tonight.
"Credit to Huddersfield, they'll be delighted with the result. They came and got everyone behind the ball, played counter attacking football, and were hard to break down."