Allardyce's West Ham beat Leicester 2-0 at Upton Park on Saturday thanks to goals from Andy Carroll and Stewart Downing.
Defeat was Leicester's 10th in a 12-match winless run that leaves them rooted to the foot of the table and facing the very real possibility of an immediate return to the Championship after sealing promotion by cruising to the title.
And it is that achievement from last season that boosted Pearson's standing in the game, a factor that Allardyce believes should buy him more time as he bids to turn the club's fortunes around.
"None of Nigel Pearson's players let him down," Allardyce told the BBC.
"They gave everything and when we went 2-0 up they caused us some problems.
"He is a very good manager and he has proved that. I hope the club are patient with him and give him some funds to spend in January.
"If you look at Leicester's results, they rarely lose by two goals, even though they haven't won any games since beating Manchester United.
"That's disappointing for Nigel, because he is a friend of mine and I want him to do better, and also because his team shows a lot of commitment. They are not too far away and only one thing is missing in their team and that's a goalscorer.
"That is eluding them at the minute and is why they are where they are, and to beat this team we had to play well."
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