Pearson told BBC Radio Humberside: "Jay's having a really tough time of being able to do what he's here for.
"He's struggled to make the impact that he wants and I want but I will keep faith with him it's a simple as that."
Simpson, who scored 13 goals whilst on-loan at QPR last season, made only one senior start for Arsene Wenger's side in a 3-0 League Cup win over Wigan on 11 November 2008.
I think psychologically that can have quite an impact on a player
Nigel Pearson on Jay Simpson's lack of goals
He also previously had loan spells with Millwall and West Bromwich Albion, managing a total of 10 goals in 81 appearances.
Pearson says he understands that the longer the barren run continues the more it will play a part in how Simpson performs.
"I think psychologically that can have quite an impact on a player, certainly a young man like him," he added.
Meanwhile, Hull are waiting to find out the extent of injuries sustained by Richard Garcia (knee) and Anthony Gerrard (calf) in Saturday's 0-0 draw at Crystal Palace.
Both players limped out of that game in the first half.
Source: BBC Sport
Source: BBC Sport