Leicester dominated the first half and were well worth the lead given them by David Nugent from the penalty spot in the 14th minute but Jamie Vardy missed a great chance to double the leader and Danny Ings levelled two minutes into the second half to earn Sean Dyce's men a point.
A frustrated Pearson said: "We missed our chances when we were on top and didn't work hard enough to stop the cross for their goal.
"You look at the game in its entirety and it was a good illustration that you have got to score when you are on top.
"We were excellent in the first half and I even think that we finished the game really well. All in all I still think it was a game we should have won. But we were playing against a very good side with good levels of resilience.
"I'm sure that Sean's pleased with the result and he might even think they could have done better. But I think our performance was pretty good.
"I am not going to complain too much but as I said it is about taking your chances. The good thing is that we are creating plenty of chances. We just missed that bit of killer instinct. We had some very, very good chances today.
"I thought Jamie Vardy was excellent and I would have loved him to convert one of his chances. That would have completed a very fine performance by him."
Dyche said: "I am pleased with a point. In fairness to Leicester they had a very good start and created one or two real good chances and will be aggrieved they didn't put them away.
"I thought we defended resolutely but were not at our best with the ball. The first goal was because we gave it away in a poor situation which is not like us.
And I thought it was a softish penalty, but it happens and I've got no problem with it.
"But I think that overall a point was probably appropriate for both sides. We both had chances to nick it but over the whole game I think it was a fair result.
"I was really pleased with the framework of the side and the way they kept their resilience and belief in what they had to do. It is difficult to win football matches especially when you are coming away to places like this.
"It is a tough division and the challenges are there every week. But we are working hard and enjoying it."
Referee Andy D'Urso pointed to the spot when Vardy went down under a combined challenge from Jason Shackell and Ben Mee and Nugent blasted the penalty past Tom Heaton.
It was Nugent's seventh penalty and 11th goal of the season.
But Vardy missed a great chance of adding to the lead when he shot wide just before half-time.
Burnley hit back two minutes into the second half, with the prolific Ings scoring his 12th Championship goal of the season from close range, after Danny Drinkwater and Liam Moore failed to clear a cross from Kieran Trippier.
Burnley were the better side in the second-half and only a great save by Kasper Schmeichel denied Sam Vokes a second goal.
But, in a frenetic finish, Jeff Schlupp and Anthony Knockaert came close to snatching a winner for the Foxes.