Simon Jordan told The Footballers' Football Show John Terry should forget about appealing his punishment from the FA and try to move on.
The Chelsea captain was found guilty of racially abusing QPR's Anton Ferdinand by a Football Association independent regulatory commission on Thursday. He was handed a four game ban and fined £220,000.
Terry's legal team have said they will wait for the panel's report to be published before deciding whether to appeal or not, but former Crystal Palace chairman Jordan says he cannot see the point in the former England defender going down that route.
"The best thing to do is put a lid on it and move on," he said. "I don't think Terry will appeal. I'd be amazed if he did.
"If he did then that would make it worse, it would prolong the scenario and there's no benefit for him in that.
"I don't think he's ever going to exonerate himself and in my experience in dealing with these bodies, if they're on solid ground and you go and challenge them, they'll make it worse for you."
Jordan also said he thinks the FA were keen to show their authority in the case, putting Terry on trial despite a court of law finding him not guilty earlier this summer.
"The big argument will be whether the FA should have taken him to task after the Crown Prosecution Service brought a prosecution against him," said Jordan.
"I don't think the two things are linked. The FA are the governing body of football and they have their own rules and regulations, they have a different burden of proof to the CPS, but I feel, equally importantly, they wanted to exhibit to the world they have their own governance over the game.
"They've dealt with it, whether the findings bear out as to whether they were right or wrong we'll have to wait and see.
"For years I have railed against the FA for being toothless. I think what they're trying to do now is get a bit of backbone, a bit of control. They've done what they think is right and at the end of the day everyone is going to have a different view."
Former Aston Villa and England defender Ugo Ehiogu told the show Chelsea and QPR should have got the two players together to clear up the issue when it happened 11 months ago.
"I don't think Terry's a racist - I think he's made racist remarks," said Ehiogu. "There's a slight difference.
"But this has snowballed and snowballed. My initial reaction was that the two teams should have brought the two players together.
"When I played, three or four years ago, we would have brought the two players together and this wouldn't have got this far."