Grabban became the first Bournemouth player to score 20 goals in a second-tier season when he netted the winner in a 2-1 victory for the Cherries against QPR on Saturday.
However, the 26-year-old's future had been uncertain in the winter transfer window when he held talks over a switch to Brighton & Hove Albion before opting to sign a new deal with Bournemouth.
And Redknapp regrets not trying to sign the player, having become frustrated by QPR's lack of potency when they have been without Charlie Austin.
"He's done well. When he looked like going to Brighton we should have snapped him up because he had a buy-out clause," Redknapp said in the Daily Mirror.
"He's full of energy, he runs behind people, stretches people. He's done great, he's a good player. I've been impressed with him.
"That's been our problem all season, We have a lot of play, but where's the goal going to come from? Who's going to score?
"People who score goals, score goals, people who don't score, never score. That's how football is. We are short of goals when Charlie Austin is out of the team."