The pair squared up to each other after the final whistle on Sunday as Spurs celebrated a 2-1 victory at White Hart Lane.
A policeman had to separate the duo as they became embroiled in an angry confrontation, with Wenger refusing to shake Allen's hand.
The Spurs man was left fuming by the actions of the Gunners manager, but insists there was no foul-mouthed exchange on the touchline.
"He refused to shake my hand," said Allen.
"He says he didn't see me or hear me - but he's two bob he is, two bob."
Asked if he had sworn at the Frenchman, Allen added: "No, I didn't call him any dirty word."
Wenger, though, hit back by pointing out that there is no rule stipulating that he has to shake hands with every member of an opposing coaching staff.
"I shook the hand of the manager and the assistant manager," he said.
"How many hands do I have to shake? Is there a prescription?
"No words were exchanged and if the story of the game is Clive Allen, you must ask him. He wanted to make himself the story, yes."
Spurs boss Harry Redknapp attempted to play down the incident afterwards, claiming that he was happy with Wenger's reaction to suffering a painful defeat.
He said: "Arsene shook hands with me and I'm pleased with that. I think Clive went to shake hands and he missed him. He didn't see him.
"But if he's going to shake hands, either do it and mean it or don't do it at all.
"If he doesn't want to, he shouldn't. Okay, Clive wasn't happy but Arsene shook my hand and, for me, that was it."