Pearson took exception to the supporter questioning the commitment of his players in Tuesday's Premier League match and suggested spectators with similar views might "stay at home".
Leicester remain bottom of the table despite leading through a 22nd-minute own goal from Liverpool goalkeeper Simon Mignolet.
Adam Lallana levelled before returning captain Steven Gerrard gave the visitors a second-half lead.
Wes Morgan's red card for a professional foul on Rickie Lambert compounded matters for the hosts, but Pearson was happy with the effort put by his team and defended them amid a flashpoint in the stands - even though Jordan Henderson added a third for Liverpool seven minutes from time.
"I had a spat with a fan towards the end," he told BT Sport. "I don't know what they are looking at, at times.
"If they cannot see the players are having a proper go maybe they need to stay at home. The players are giving everything.
"I will always look for the positives. It is very easy for people to look at what we are not good at.
"I don't like the commitment of my players being questioned. If they honestly think they are not committed, they are very wrong. Maybe that is why I stay in the stand."
Pearson acknowledged that Morgan's sending off was a key moment against last season's runners-up, but believes his squad has the quality needed to turn around a winless run that now stands at nine Premier League matches.
"We can ill-afford to play any game with anything less than 11 v 11," he added. "Their third goal knocked the stuffing out of us.
"We have quality and commitment. We can't get downbeaten by tonight's result. We have to break the cycle we are in at the moment."
