Pearson said: "I'm pleased we are still in the play-off picture but I am sure there are 10 or 12 managers who think they still have a chance.
"It's very tight and it only takes a couple of bad results to drop out of it.
"Sheffield United would have been one of the favourites to go up before the season started and that's why I'm delighted with the win.
"I thought we started the first half poorly and it took us 10 or 20 minutes to get going. We made some poor decisions early on but then we got it together to play some decent football.
"I thought we played very well after a poor start and created some good chances. We were worthy winners in the end."
The Leicester boss also praised his side for how they handled a forced defensive reshuffle at half-time after the injured Jack Hobbs was replaced by youth academy product Luke O'Neill.
"Hobbs had a dead leg early on and so we had to reshuffle at half-time but the way we handled it all was testament to the players' application."
United boss Kevin Blackwell tipped City as promotion challengers.
He said: "I've said from day one that Leicester will be in the mix. They are there on merit and show every sign of finishing the season in the top six."
Blackwell pointed the finger of blame at unnamed players after defeat at the Walkers Stadium ended his side's six-match unbeaten run.
He said: "I think some of the players turned up thinking they would have an easy Boxing Day out at Leicester and that complacency was our worst enemy today."