Derby County were beaten 2-0 at Oakwell on Saturday
Despite having much of the ball in their Championship clash and more shots on goal, the Rams lost out to goals from Alfie Mawson and Rams' keeper Scott Carson, who put the ball into his own net.
Some of Derby's 4,000 strong contingent voiced their discontent at the result and performance after the final whistle in Yorkshire, and that was not missed by Pearson.
Pearson will hope to put things right, and quickly
But the former Leicester boss appreciates the supporters' disgruntlement at Derby's display, with the Rams yet to find the net this season.
"We don't like the fact that people are going to be critical but I think people are well within their rights to be critical because we did not perform anywhere near the level that we should do.
"I understand the fans' frustration.
Derby County manager Nigel Pearson (L)
"It is always disappointing to lose games but I don't like losing in the fashion that we did.
"We didn't show what we are about, we didn't give the right sort of messages.
"I have been in this position before. I know what it's like to be in this sort of situation and when people question your application that's something we need to take very seriously."
Richard Keogh scored Derby's winner against Grimsby during the week
Derby drew their opening day clash with Brighton at the iPro, earning a 0-0 draw against Chris Hughton's side.
They did manage a win in the EFL Cup first round, overcoming Grimsby 1-0, but they will hope to bounce back from their Barnsley defeat with a positive result on Tuesday when they take on Preston at Deepdale.