The 26-year-old scored his 20th goal of the season on Saturday as the Cherries beat Redknapp's side 2-1 at Dean Court.
Grabban held talks with Brighton & Hove Albion over a potential move in January before deciding to sign a fresh deal with Bournemouth, but Redknapp has said that he should have attempted to sign the forward.
"He's done well. When he looked like going to Brighton we should have snapped him up because he had a buyout 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."
Grabban joined Bournemouth from Rotherham United in 2012.