Having ended their 565-minute goal drought through Michael Kightly, Burnley still found themselves 2-1 behind going into stoppage time at the King Power Stadium.
However, a 96th-minute free-kick from Ross Wallace was too good for Kasper Schmeichel and earned the visitors a point that Dyche felt their performance deserved.
Burnley, without the influential trio of Dean Marney, Danny Ings and David Jones, fell behind after Jeffrey Schlupp netted.
Riyad Mahrez, who created Schlupp's opener, edged Leicester back in front following Kightly's leveller before Wallace's late heroics.
"I thought they were terrific from start to finish, it was the least we deserved," said Burnley boss Dyche.
"There were two sloppy moments, certainly the second goal in particular, but I thought they were absolute excellent.
"It was much more of a reminder what we're about because we've only come away from it once, last Sunday [a 4-0 defeat at West Brom], when we didn't look at it.
"This was completely different. We started with a will and demand, some good play, we looked effective going forward, we looked solid, mostly, although we were disappointed with the two goals.
"The manner was back, the way we go about our business, the demand, the tempo and the belief in the play.
"It's a tremendous thing to see when you see a group who were not as strong as we could be. We've got injuries and challenges.
"We made changes, and we had to, and yet the group accepted that and went about their business in that manner."
The point lifts Burnley off the foot of the Premier League table as the Lancashire club climbed above QPR.
