Diouf is being investigated by Merseyside Police for alleged racial abuse of a 14-year-old ball boy at the match.
Diouf told police after the final whistle - and repeated the claim on Monte Carlo Radio - that bananas were thrown at him from the Everton crowd.
Officers immediately scoured the area next to the pitch and in the stands but no bananas were found. No pictures have surfaced to back up his claim either.
Everton's director of communications Ian Ross told talkSPORT that Diouf's claims about bananas being thrown were false.
He said: "That is a wholly false allegation and I really would like him to retract that allegation and apologise to the supporters and staff of this football club."
Ross added: "I don't think there's a worse allegation in modern sport than racism and it works both ways. At the moment, and from my perspective, it looks like Mr Diouf is accusing Everton fans of racist behaviour.
"The police will tell you that is completely untrue and in such circumstances we would expect him to apologise and retract his allegations.
"We would like a retraction and an apology because they are completely groundless.
"We find them offensive and a lot of our supporters have been in touch with the club to say that they find them offensive."
Ross stressed Everton would have acted on the claims if they had found any supportive evidence.
He explained: "In the same way we wouldn't tolerate our supporters racially abusing a supporter, a member of staff or a footballer in the stadium, we don't really like the idea of a visiting footballer levelling that accusation at our supporters.
"We moved very quickly and had the allegation held any water at all, we would have said so.
"And the police certainly would have said so because we work very closely with their hate crimes unit through ourselves and through our community section, the Everton Foundation.
"But the police have confirmed today that the only investigation ongoing is into the allegations against Mr Diouf, not allegations of misbehaviour by Everton fans."