"That is disgusting, there's no place for that in the game," Redknapp said. "When I was a player at West Ham we had that every week with Clyde Best because he was a black player. It was disgusting.
"He was a fantastic fella and a great player and he was the first real black player to really, apart from maybe Albert Johanneson, to make it. But it's all over, surely we can't have that sort of behaviour.
"Anyone who does it should be put to prison - not banned from football. Stick them where they belong in the nut-house somewhere. It's wrong."
Redknapp has a zero-tolerance attitude towards racism and also feels strongly about chants aimed at the family or personal life of players.
"There is other stuff that goes on as well that is sick," he said. "I hear things, I listen to the radio people talking about chants and singing songs to people at different clubs that just turns me over, I can't believe.
"You've got to be some kind of nutter to do that. That's not banter, that's sick. Sick. They're sickos who've got to be locked up somewhere. Put them away and don't let them come to football anyway."
Redknapp has seen the emergence of black players in the top flight over the last 30 years, meaning racial abuse should be a thing of the past.
"It just can't happen any more because without the black players you wouldn't have teams - because they're full of fantastic black players, everywhere all through the leagues," he said.
"I mean, how can supporters give grief to black players on the other teams when they've got them in their team. It can't happen."