Allardyce was dismissed less than a month after new Indian owners Venky's completed their takeover, with the club lying 13th in the Barclays Premier League. Redknapp was stunned by the decision and believes Allardyce will be a tough act to follow.
"He's top class at his job, I really mean that," Redknapp told BBC Radio Five Live. "People who don't know him see this big northern ex-centre-half who they think is a big hammer thrower, well he's the brightest guy you could ever wish to meet."
He added: "He is so far in advance in all the sports science and technology and preparing his teams, he is just amazing. I know him well and he has so much to offer. He will bounce back."
Redknapp added: "When new owners come in they've all got mates or have heard of someone who is good... they haven't got a clue really.
"I see Maradona's name has been mentioned... If they make the wrong decision I can see Blackburn being bang in trouble this year.
"He (Allardyce) is going to be a very difficult act to follow."
Former Blackburn boss Tony Parkes also believes Steve Kean has a big job trying to win over the players following Allardyce's exit. Scottish coach Kean is due to take the team for the first time on Saturday against West Ham after being put in temporary charge.
Parkes told talkSPORT: "It is a tricky role. When I took over you had to make sure you got the players together and everybody started with a clean slate. If you win them over you have got every chance of getting good results early. You might then just give the owners hope of getting the manager they want.
"If you lose games quickly there might be a panic job, maybe getting a new manager in within days and all of a sudden he may not be the right one that you want."
Source: PA
Source: PA