Jeffrey Schlupp and Riyad Mahrez looked to have put Leicester in control of proceedings as they scored either side of Michael Kightly's 39th-minute strike.
However, Leicester were unable to make their first-half dominance pay and eventually Burnley found their range as Ross Wallace netted a free-kick in the sixth minute of stoppage time.
Pearson lamented a frustrating end to an outing he thought the newly promoted Leicester had controlled enough to earn all three points.
"We should have won the game, we did enough to win the game," he told a post-match media conference. "But in the end we conceded in the 96th minute.
"I'm annoyed today, not disappointed, I'm annoyed.
"We should win the game, I think we're better than we were last year and I don't think they are as good as they were last year.
"They'll be pleased because they've got a result with all the injuries that they've got, but ultimately we should have won the game today.
"We've over-achieved in some games but today we've not capitalised on the situation we've found in front of ourselves. We've been in front twice, we should have won the game."
