Sullivan released a statement to talkSPORT regarding the club's situation and their disappointment with critical chants from fans.
He has now confirmed that a club-record bid went in for Allen but was rejected.
An offer of £25m was made to Stoke for Allen - and was rejected last month.
Meanwhile, Javier Hernandez is reluctant to criticise his teammates over the lack of chances being created.
Irons boss David Moyes has stated they must do more to give Chicharito a chance in front of goal.
But the striker said: "I do not like to talk about myself.
"The reality is that many things were missing (against Brighton), one of them, obviously, that we practically did not have any chances in the second-half, but I think that nothing else was that, it was a set of circumstances that we have to pay attention to next week to work well and not repeat mistakes against Watford."