Friday saw Pearson's men fall to a 2-1 home defeat at the hands of Tottenham, a result which extended their winless run in the top flight to 13 matches.
Leicester have lost each of their last six, and come into Sunday's meeting at the KC Stadium five points adrift at the bottom of the table.
"We will keep going. You can never submit to the negativity from external avenues," he told BBC Sport.
"We have to make sure we remain positive of what we are capable of. We have to keep knocking until the door yields. At the moment we are finding life very tough because the margins are so tight.
"That is the harsh reality of the Premier League. To stay here we have to up our level and resilience, and I have every faith in the players to do that.
"All the games are crucial now, but because our next game is against a side around us, we've got to go to Hull City aiming to win."
Hull had been on a torrid run themselves, with no win in 10 until Friday's 3-1 success at Steve Bruce's former employers Sunderland.
"It's been difficult and it's still going to be difficult," he said. "Make no mistake, we're a second season into this division, and we're playing teams who've been in the Premier League for years."
Mohamed Diame (knee) and Michael Dawson (hamstring) remain out, while James Chester picked up his fifth caution of the season at Sunderland and will serve a one-match ban.
Leicester could see Esteban Cambiasso return to the starting XI after he was an unused substitute on Friday.
Pearson is still without goalkeeper Kasper Schmeichel (broken metatarsal), while Matthew Upson (ankle) and Chris Wood (illness) both missed the clash with Spurs and are doubtful.
