Mackay was appointed Wigan boss on Wednesday despite an ongoing Football Association investigation into racist, sexist and homophobic text messages sent during his spell in charge at Cardiff.
The revelations saw a move to Crystal Palace fall through in August, but Wigan chairman Dave Whelan has offered Mackay a route back into the game despite criticism from anti-discrimination groups.
"I am sure his life has been hell for the last few months," Redknapp said.
"He has made a mistake but lots of people make mistakes in life - half the people who judge him have probably made more mistakes.
"It is easy to kick someone when they are down
He has got a second chance now
He has got the backing of the chairman and hopefully he will do well.
"He made a big mistake - you can't do what he did, and he has accepted that
He has apologised I am sure he has learned from that."
Former Wigan striker and now anti-racism campaigner Jason Roberts wrote on Twitter he was "disappointed" with the Latics' decision to install Mackay.
The club have reportedly inserted a clause allowing them to cancel the contract should the FA find their new manager guilty, and Redknapp gave the former Watford boss his full support.
"Whenever I have met Malky, I thought he was a decent person and a good football manager," Redknapp said.
"I get stupid messages from people all the time, silly jokes
I hate them and delete them straight away.
"But people do tend to do that in life, so he is not the only person who has made a mistake.
"He realises he has made a massive mistake and hopefully he will not make any more mistakes."
Redknapp added: "I am not condoning what he's done but he has got another chance
People get second chances in life.
"Have a look around the world and see what happens
There are people who come out of prison who have murdered people, beat up old ladies - they get second chances.
"Dave Whelan knows he is going to get stick, but it is his football club and he has done what he believes is right."
Cardiff manager Russell Slade has said he "will do things professionally" when he comes up against Mackay at Wigan in February
The 42-year-old Scot admitted the messages were "disrespectful of other cultures" and Cardiff's Malaysian owner Vincent Tan said in September he had "no sympathy" for Mackay after the revelations saw him miss out on the Palace job
Cardiff have said they do not plan to make a statement following Mackay's appointment at Wigan while he is still currently the subject of an FA investigation, and Slade adopted a similar stance ahead of his side's Sky Bet Championship game with Reading on Friday.
"The club are making no comment on that in view of the investigations that are ongoing," Slade said.
"That's our take on that matter at the minute and I really don't want to make any comment on it.
"I knew I would get asked the question, of course I understand that
But it's not the club's business anyway, other than there are on-going investigations."
Asked if he would shake hands with Mackay when Cardiff visit Wigan in the league on February 24, Slade said: "I will do things professionally as I always do.
"But it's not my issue and it's not really an issue for the club now
It's an issue for the FA.
"It's not (a hindrance)
The moment I walk out of this room my total focus will be on Reading and our next game."
Source : PA
Source: PA