Big Sam was booed by Hammers fans during victory over Hull City last week.
Nolan said: "I don't understand all the talk that Sam is just here to keep us up. We finished 10th last year and we did it comfortably. He is just not that kind of manager."
Nolan then pointed to the respective fortunes of two of Allardyce's former clubs after they opted to change boss.
He added: "Sam left Newcastle and they were in the top 10 - 18 months later, they were relegated. He then left Blackburn, and 18 months later they were relegated.
"To be honest, I am fed up trying to tell people what kind of manager he is. His record is there for everyone to see. He gets criticism, which is very unfair."
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