Albion chief executive Martin Perry is to take action after a bottle was thrown on to the pitch during Saturday's game.
The incident marred the Seagulls' 4-3 victory over Cambridge United at Withdean Stadium.
It came after Luke Guttridge scored for Cambridge to level the score at 2-2 in the second half.
Team-mates joined in the celebrations in front of the South Stand, where most of the Albion's fans were gathered.
The bottle did not hit anyone and a steward retrieved it before the game kicked off again.
Sussex Police said yesterday they had no record of a complaint about the incident."
He was due to call for a club report into the incident this morning and was not prepared to discuss the matter until then.
Mr Perry and club officials are determined to stamp down on any trouble from Albion fans.
He warned them about their behaviour after Chesterfield officials and supporters complained about their experiences at Withdean on December 21.
In a match programme, he said bad behaviour by fans was totally unacceptable.
Chesterfield complained Albion fans had used abusive language against the visiting side and had stood for long periods during the game blocking the view of others.
Mr Perry urged Albion supporters not to let the club's reputation for a warm and friendly atmosphere slip.
He said: "The achievements of our club over the last four years have enhanced our reputation nationally.
"Please help us maintain that name for friendly home support by keeping up the high standards of behaviour we have enjoyed at Withdean during the last two and a half seasons."
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