Pompey could have climbed to fourth in the table had they recorded their fifth consecutive league win, but Rob Green's plunging save to his left denied the Zimbabwean his sixth goal in four games - and his eighth this season - after Hammers defender Danny Gabbidon was harshly ruled to have handled.
Redknapp also saw striker Kanu miss a spot-kick when Liverpool's Jose Reina saved in last month's goalless draw - the only other time Pompey have failed to win at home this season.
"(Niko) Kranjcar or (Sulley) Muntari were down to take any penalties. I wish one of them had.
"Kanu went on as substitute but I've already told him to stop taking penalties after the Liverpool game."
Redknapp added: "I saw Niko with the ball and I was happy with that but Benji must have taken it off him.
"Of course I gave Benji a rollicking. I said 'you are a silly boy' and told him off - but he does so much work that I wish I hadn't rollicked him now. He's been in great form."
The Pompey boss backed referee Mike Dean's controversial decision to award the spot-kick.
He said: "I thought it was a penalty. Gabbidon touched the ball and moved it on with his arm, but coming so late in the game it has got to be a bit harsh.
"West Ham played well and matched us up in midfield. They must have done their homework but we started strong and if we'd scored it might have given them problems.
"But it is another clean sheet, another point and we've had a great month.
"It was a tight game and they played the same system as us. It is difficult to break down and we are going to get a lot of games like that here now."