The 51-year-old was involved in a verbal altercation with the fan during the 3-1 defeat at the King Power Stadium, with Pearson seemingly taking exception to the team's committment being questioned.
After the match manager Pearson confirmed the disagreement and suggested those with similar opinions should "stay at home".
The former Hull City boss attempted to clarify his stance at a pre-match news conference ahead of Saturday's clash with Aston Villa, but was adamant there would be no apology forthcoming.
"Apologise to who? No, I'm not apologising to him. I've had run-ins in with fans in the past and sometimes, heat of the moment, these things happen," he said.
"But there certainly won't be any apology, let's put it like that."
Leicester are on a nine-match winless run that stretches back to September's thrilling 5-3 victory over Manchester United.
Pearson said he could understand why supporters were unhappy with results, but believes those frustrations should be aired in an appropriate manner.
"It depends on how they [fans] do it [voice frustrations]," he added. "I'm not saying they can't, but then they can't bleat on about it if they get a taste of their own medicine.
"I don't think everybody is totally frustrated with how we're playing, they're frustrated with the results."
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