City came into the game off the back of five successive wins and looked to be on course to make it six after Ben Marshall put them ahead early in the second half.
But goals from Davide Petrucci and Grant McCann - the second coming two minutes from time - consigned the second-placed Foxes to defeat, leaving them level on points with third-placed Watford and Hull, in fourth.
Pearson admitted: "There's no doubt it goes down as a missed opportunity. When you get in front in a game like this, you have to close it out and we failed.
"We certainly created enough good chances to do that but I felt we didn't work hard enough to keep a clean sheet at the other end.
"That is not something you will hear me say about my players too often but I felt Peterborough had more drive than us, especially after they had got themselves level.
"You have to give them some credit for the way they finished the match."