Pearson's side remain rooted to the bottom of the Premier League table after Joe Ledley scored the only goal of the game with a header early in the second half at the King Power Stadium.
Leicester saw David Nugent head against the crossbar and also passed up chances from Riyad Mahrez, Jeffrey Schlupp and Paul Konchesky before Julian Speroni twice denied Jamie Vardy late on.
"The thing that's cost us today is the inability to convert the chances that we have created," said Pearson.
"The big issue that we have is our inability to take our chances when they come along and that is the ultimate difference between the Championship and the Premier League.
"On today's performance and chances created, we should have got at least one point out of the game, if not three. We've got nothing."
Pearson was busy in the January transfer window but was without on-loan Robert Huth against Palace as the central defender was suspended.
He started the game with another recent signing in Mark Schwarzer in goal but left forward Andrej Kramaric on the bench until the second half.
Despite the defeat, a defiant Pearson said: "I have to keep working with the players to turn it around. We've got a lot of good players here but time is the one thing as a manager or as a player you don't get.
"There’s still and awful long way to go and if people feel the need to say today's a defining moment in terms of the season, well not necessarily. We're not going to get downbeat by how people possibly want to write us off after a result like this."
