The pair were involved in a touchline spat after Spurs beat North London rivals Arsenal 2-1 yesterday (Sunday), with witnesses reporting an angry confrontation.
"He [Wenger] refused to shake my hand," Allen said later. "He says he didn't see me or hear me, but he's two bob, he is."
Wenger shook the hands of Spurs boss Harry Redknapp and assistant manager Kevin Bond, but then headed for the tunnel – chased by Allen, who was angry at the snub.
"I shook the hand of the manager and the assistant manager," Wenger explained. "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."
A stand-off in the tunnel led to the intervention of the police, who had to restrain Allen.
Later, Redknapp came to the defence of Wenger.
"Arsene shook hands with me and I'm pleased with that," the Spurs boss said. "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.
"Clive wasn't happy but Arsene shook my hand and, for me, that was it."
Wenger and Allen have clashed before – after the teams' 3-3 draw at White Hart Lane last season, Allen was accused of shoulder-barging the Frenchman.