Andy King's late strike at the King Power Stadium sealed a much-needed win for the hosts, lifting them to within four points of safety.
Pearson is confident his side - who saw David Nugent miss a penalty after Esteban Cambiasso's opener had been cancelled out by Cheikhou Kouyate - have the right mentality to get out of trouble.
"It's been a frustrating time for us," he said after Leicester's first win since January.
"Frustrating times test your resolve, but today we deserved it. Players had some doubt after the penalty miss, but responded [in the] second half.
"We beat a very good side today, but let's not get carried away with one result. We must look to the next game and ensure we're ready.
"The Premier League is a difficult place to be a success in, but we'll be working hard to retain our status.
"I saw players out there in Leicester shirts that showed a lot of belief. We have eight games to give us the best chance of staying up.
"It is still a big ask for us to achieve retaining our Premier League status, but we've got five at home and have got to give ourselves the best chance by performing as positively as we have done today.
"The players have a shared goal, and success is to get us out of the mess we are in."
