Spurs were stunned by a goal from Pompey striker David Nugent on the break coming out in the second half but came back strongly and equalized in the 70th minute through Jermain Defoe.
The home side then went on to lay siege on David James' goal with the best chance falling to Bent who managed to send his header wide when it would have been easier to score.
Reports from The Sun claimed that a red-faced Redknapp punched the air in anger and let slip what he thought of the shocking miss.
He screamed: "How the f*****g hell did he miss that one?
"You will never get a better chance to win a game. Even David James had given up on it and was walking backwards into his own net.
"Bent didn't only have part of the goal to aim for but the entire net... and he puts it wide. Unbelievable.
"I was just so frustrated because I could see the ball dropping on his head and if it goes in, then it's goodnight Portsmouth. Game over and three points in the bag."
Bent has been left on the bench since Jermain Defoe re-signed for the club but came on in the first half due to an injury to Roman Pavyluchenko in the first half.
Whether the former Charlton striker will stay or be sold after Redknapp's tirade remains to be seen.