David Norris opened the scoring for Pompey on 68 minutes before David Nugent levelled for Leicester, while Kasper Schmeichel produced top-draw saves to deny both Norris and Hayden Mullins as the visitors held on for a point.
Pearson said small margins will decide who will secure promotion from the npower Championship this season, and he told his players that they need to learn to win close games.
"Ultimately, we need to raise the bar somewhat and strive to win tight games like this," he said.
"The fact we have been waiting for back-to-back wins for a considerable time shows why we have not really asserted ourselves on the league yet.
"When we conceded the goal, we were fairly comfortable, so that was disappointing. But the players showed really good courage and application to get back into it."