Mackay and his former head of recruitment Iain Moody are alleged to have shared racist, sexist and homophobic texts when they worked together at the Welsh club.
The Scot has apologised for the messages he sent but drew further criticism after a statement issued on his behalf by the League Managers' Association on Thursday night said they were intended as "friendly text banter". The LMA has subsequently apologised for the tone of its first statement.
News that the Football Association was investigating the exchange prompted Crystal Palace to drop their interest in appointing Mackay as their new manager, but Redkapp does not believe these allegations "should finish his life".
"What I would say is that Malky Mackay has made a big mistake," Redknapp said.
"I don't know the other lad (Moody) but what they have done is not right. Malky is a great lad, a family man and a real football man, he has made mistakes and people make mistakes in life.
"Suddenly everyone is an angel, he made a big mistake the lad but it shouldn't finish his life. He is a good manager and I feel bad for what he has done but I bet no one is feeling as bad as him or his family today.
"I'm not condoning what he has done but show me someone who has ever made a mistake and I will show you a liar. He hasn't murdered anyone, he hasn't raped anyone and he is not a paedophile."
With the cloud hanging over Mackay it could be difficult for the former Norwich and West Ham defender to find another managerial position any time soon.
But Redknapp wants to see him given a reprieve at some point in the future: "It is going to take time," he said.
"People get second chances in life who have committed bad crimes - he has made a mistake but we aren't going to hang him for it are we?
"Hopefully he will learn from what he has done but everyone does the tweeting and texting. I don't send text messages, but I do receive them with sick jokes. I don't read them, they make me ill.
"He is a good person underneath all that and I hope he comes back, I can't feel how he must be suffering for the big mistake he has made."
Former PFA chairman Clark Carlisle, who played alongside Mackay for two years at Watford, called for the Football Association to take a "strong and efficient stance" over the issue.
Carlisle told Press Association Sport: "You will struggle to find anybody in the industry who has worked with or played against Malky who has a bad word to say about him.
"But everybody has to separate their opinions as Malky as an individual from the severity of the issue, and the fact is that the FA has got to take a strong and efficient stance on this, by conducting an investigation and reacting accordingly.
"It has to be reiterated that there is no place for language or sentiment to prejudicial thinking in the game, and if Malky is found to have fallen foul of those standards then he needs to face the consequences."
Carlisle described the League Managers' Association's initial statement in support of Mackay as "incredibly poorly worded", but stressed it ought not to deflect from the real issue which is to continue the fight to banish such incidents from the game.
Carlisle added: "It is shocking that our national governing body does not have a distinct protocol in place whereby when such incidents take place there is an exhaustive but efficient protocol to go through."
This is brilliant! All these years of moral ambiguity, grey areas of offence and context..now we have a simple, easy to follow guide to right and wrong. "What did you do today?" "I kicked the face off a panda". "Oh well, you didn't rape, kill anyone or abuse a minor, knock yourself champ."- megabrow (cufc)