The Daily Mail says Nolan could be stripped of the captaincy after he was sent off for lashing out at Fulham's Fernando Amorebieta.
Allardyce said he will review Nolan's captaincy, admitting he cannot fathom his long-term chief lieutenant's recent behaviour.
"I just don't quite understand where he's lost his cool and why it's happened," said Allardyce, who saw his side squander an early lead.
"I know the centre-half fouled him, and I also know that (referee) Mark Clattenburg didn't give a free kick and he should have done.
"But it's still not an excuse for what Kevin did, and he ends up getting himself sent off."
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