A Curtis Davies own goal saw Leicester take an early lead at the King Power Stadium before Nikola Zigic equalised just after the hour mark.
Jeff Schlupp then looked to have ended their eight-match winless run when he headed them back in front only for Birmingham substitute Chris Burke to score a last-minute penalty after David Nugent was adjudged to have fouled Wes Thomas inside the area.
Pearson's side must now play eighth-place Bolton on Tuesday night followed by games with Crystal Palace, Watford and Nottingham Forest, sides who are currently fourth, third and fifth in the table respectively.
"We probably have to win all four of our remaining matches now. It's do-able," said Pearson.
"We've got to win the next game, but then we've been saying that for a while now.
"We've created enough chances to win this game comfortably and really we should have won the game.
"After Brighton at the weekend, that's two games running now that we've conceded equalising goals late in the game and had to settle for a draw.
"It's difficult to swallow. The mistakes that we are making at the moment are costing us dearly."