Harmison unintentionally struck Ponting in the face with a bouncer in the first Test at Lord's that sneaked through his helmet guard and drew blood, signalling England's intentions to take the Australians on at their own game.
Ponting recovered quickly but Harmison said he still regrets his immediate response and for not apologising to the Australian captain at the time.
"That was unfortunate. It's probably one of the biggest regrets I had from that whole series," Harmison told reporters.
"As a group of players I think we could have handled it better. As a bowler and as a person I'm disappointed with myself the way it came about.
"I'm a fast bowler and the ball does come out of my hand at decent speeds and does bounce, it is a dangerous thing. Nobody likes to see someone get hurt."
Harmison said he was initially unaware that Ponting had been cut and by the time he realised, it was too late to apologise.
"The silence was enough. By the time I got back to my mark the opportunity had been missed and I didn't want to drag it up. It was best left alone to be honest," he said.
"It was one of those unfortunate things that happened. I don't think it's going to stop me form bowling short balls at anybody and slowing up because of it.
"I'm not somebody who's in the business to hurt people."
Ponting has said he harbours no ill-feeling towards Harmison over the incident during a series which was marked by extraordinary sportsmanship.
While the action on the pitch was always intense, there was not the slightest hint of animosity between the players, who became good friends off the field.
"That's how sport should be played as tough as it is and mentally draining as it was on the field from 9am to 6 o'clock that night and then as human beings you could have a drink afterwards and chat and you can be friends," England batsman Kevin Pietersen said.
"I think that everybody learned from last year of how much sportsmanship there was in last year's series and I don't see any reason why anybody should be fighting, shouting and complaining at each other."
