Pearson returned to Brunton Park for the first time since he was in charge of Carlisle when Jimmy Glass scored the last-gasp goal that kept them in the Football League in 1999.
"They caused us problems. They worked hard and pushed us all the way and they played with quality as well," he said.
"They put on a good performance. They'll be disappointed not to get anything out of this but I've no apologies. I thought we were worthy winners in the end. I think we created more chances and overall were the better side."
Danny Graham opened the scoring for the home side in the 27th minute. After he was fouled just outside the box, Leicester failed to clear Graham Kavanagh's free-kick and Graham forced it past Dave Martin from close range.
The Leicester midfielder Andy King levelled the scores in the 59th minute when he lashed in a fierce shot from just outside the box.
And 10 minutes later Leicester took the lead when the Switzerland international Bruno Berner forced the ball home following a corner.