Leicester headed to Selhurst Park on the back of an incredible 5-3 victory over Manchester United last Sunday.
However, last season's second-tier champions were undone by second-half goals from Fraizer Campbell and Mile Jedinak against Neil Warnock's side.
Leicester arguably edged the early stages and could have gone ahead in the 13th minute when Jamie Vardy saw a shot from inside the area saved by Julian Speroni.
A dogged Palace defence kept Leicester at bay, though, and manager Pearson believes his team must take their chances when they come.
"No doubt in the first half we looked pretty comfortable. It was about half an hour before they had a serious threat on our goal," he said.
"In the second half we didn't have enough control. It illustrates we have to take the chances when they come along. We had good opportunities but couldn't convert them and sometimes you pay the price for that.
"We didn't take the chances that came along and you have to give Palace a lot of credit, they defended their goal with numbers and the match didn't go our way."
Both of Palace's goals came from set-pieces and Pearson rued the number of soft fouls conceded by his team.
"We didn't defend the set-plays as well as we have done in previous games," he added. "The quality of the delivery was pretty good, they have some big players and we didn't quite deal with it.
"There will be individual errors but for the most part what you have to do against sides who put high emphasis on set-plays is not give them away.
"I thought at times we were guilty of giving away a couple of cheap ones, we could have taken pressure off ourselves by not giving them away."
Leicester remain in the top half and face fellow top-flight newcomers Burnley next Saturday.
