Adam Clayton and Sean Scannell were on target for Huddersfield as the Terriers booked a date with Premier League Wigan in the fifth round.
Michael Keane replied for Leicester to make it 1-1 but that was a lone bright spot for the home side, and 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.
"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. But we did not look as dangerous as we have been.
"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."