Mr Paisley later contacted then Prime Minister David Cameron to lobby on a UN resolution concerning Sri Lanka and is set to be suspended from the Commons for 30 days.
Mr Wells had the DUP whip withdrawn after he claimed the party broke a promise to reinstate him as Health Minister, a claim the party denies.
He declined to say if he thought Mr Paisley should be suspended, but said that if he had behaved in the same way as Mr Paisley he would have been "for the high jump".
"I'd be gone. But, I'm me, Ian Paisley is in a different position because of the strength within his constituency," the South Down MLA said.
TUV leader Jim Allister also appeared on the show and said it would be unfair if the party took a different approach to the one taken with Mr Wells.
"Why should that be? Either right is right and wrong is wrong or it's not. Why should there be a difference made according to who you are," the North Antrim MLA said.
"I think this is the real challenge to the DUP, are they going to stand up and do what's right or are they going to endorse this.
"Lets say there was a by-election and Ian Paisley was the candidate, unsuspended, undisciplined, in respect of this. Are the DUP going to say to the voters of North Antrim this is what we endorse, this is what we embrace. Is Arlene Foster going to be down campaigning saying 'vote for your Sri Lanka visiting MP'?"
Mr Wells said that although Mr Paisley had clearly done wrong his constituents were still behind him.
"I have absolutely no doubt, even based on what Ian himself has said that what he has done is unacceptable. He has made a ghastly mistake.
"I was in North Antrim most of yesterday (Wednesday) and I can tell you there is absolutely no appetite for a by-election.
"He is one of the hardest working MPs at Westminster. I would wonder could I ever match him in terms of his constituency output."
Mr Paisley's father Ian senior was his predecessor as North Antrim MP and Mr Wells said that the family remain popular in the area.
"The Paisley family have given 48 years of service to North Antrim, there's not a single family in North Antrim who has not had some benefit from the Paisley family," he said.
"Everyone I've spoken to in North Antrim, not one person can lay a finger on Ian in terms of his constituency work.
"North Antrim was one of the most strong pro-Brexit constituencies in the United Kingdom and there's not a person there who cannot say that Ian Paisley has not represented his constituents fully on the issue.
"He has been excellent in his representation of the Brexit cause and I think that's part of the reason there is such a clamour for his head today."