The Hammers collapsed in the final 30 minutes to lose 3-1.
Afterwards, a reporter asked Pellegrini if he believes he is the man who can revive this struggling squad, he was adamant he is, before the interview ended abruptly at the close of questioning.
"I always think I can fix," he said. "(My future) does not depend on me. I don't think nothing because it doesn't depend on me."
Monday's defeat means West Ham have now lost three in a row at home in the league for the first time since August 2015.