The Foxes dominated the first half and were well worth the lead given them by former Claret David Nugent from the penalty spot in the 14th minute but Jamie Vardy missed a great chance to double the lead and Danny Ings levelled two minutes into the second half to earn Dyce's men a 1-1 draw.
"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," said Dyche.
"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.