Foxes new-boy Chris Wood scored two goals on his debut, Anthony Knockaert also netted twice and Ritchie De Laet and Martyn Waghorn completed the rout.
The Terriers, completely outplayed from start to finish, snatched a consolation goal through Scott Arfield.
"We wanted to start the new year in a positive manner but this could not have been any worse for us," said Grayson.
"We wanted to be hard to beat and make sure it was a difficult afternoon for Leicester and make sure they didn't have an easy ride.
"But the way we started the game allowed them to dictate to us what they wanted to do. And before we knew it we were a couple of goals down and too many times made the wrong decisions. The third goal probably summed us up when we decided to play kamikaze football across the back.
"At half-time we talked about restoring some pride and respectability but before you know it we are four goals down and it becomes a real hard slog.
"As a team we didn't play well enough and made poor decisions against one of the best, if not the best, team in the division.
"We were lacklustre and architects of our own downfall."
- Sports & Recreation
- Ritchie De Laet
- Martyn Waghorn