Palace never got into their passing rhythm in the freezing conditions and their inability to put pressure on their opponents contributed to a dour affair.
The hosts will feel they should have secured their place in the next round as they wasted a number of decent chances.
Leicester have been unstoppable of late and lie top of the League One table - winning eight home matches on the trot - and they went close to breaking the deadlock with Steve Howard and Max Gradel guilty of bad misses.
Pearson said: "It was an opportunity today to see how we compare against a Championship side and I thought we did pretty well. We were never under too much pressure and always looked the likeliest to score.
"It was a game of few chances but it was always going to be like that because Palace are a very organised and competitive side.
"But I thought we had the better opportunities and the lion's share of the play and performed pretty well.
"We could have done without a replay, but a replay is better than a defeat."
Palace manager Neil Warnock felt a draw was a fair result.
"No one deserved to win with the systems both sides played. There was never going to be many chances and you felt a mistake was the only way anyone was going to win it."
Warnock was fulsome in his praise for Leicester.
"It will be good to see Leicester back in the Championship because they are a good side," he said.
Leicester's best chance of a drab encounter came on the hour mark when substitute Paul Dickov played an incisive pass to Howard who shot wastefully wide from 10 yards with just the goalkeeper to beat.
On 81 minutes Gradel cut inside a defender and then unleashed a fierce 20-yard shot which Julian Speroni needed two attempts to smother.
Joe Mattock saved City with five minutes left when he flung himself in front of Neil Danns' goal-bound drive.