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 said. "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 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 on BBC Radio Five Live: "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."
Source: PA
Source: PA