Controversial Italian Balotelli, a second-half substitute, had already been booked for a foul on Benoit Assou-Ekotto when he tangled with Parker in the 84th minute.
Balotelli twice caught Parker, who was flat on his back, the second time square in the head as he seemed to lose his balance and fall over.
The officials gave Balotelli the benefit of the doubt and accepted his claim that it was an accidental coming together but, after the Italian settled the game by winning, then converting, a 94th-minute penalty kick, Redknapp was less generous.
“Yes, I do think that,” said Redknapp when asked if Balotelli should have been sent off. “It’s not the first time he’s done that, is it? I’m sure it won’t be the last.
“I’m the last person to talk about getting people sent off, but it’s blatantly obvious if you see that, he reacts like that at times to challenges.
“Scott has a lovely cut on his head. I’m not sure if he’s had stitches, but that’s how it goes sometimes. I’m surprised the linesman hasn’t seen it. The first (stamp) could be an accident, but the second one? He’s back-heeled him straight in the head.
” … Whether he gets sent off or whatever, it’s wrong and I don’t like seeing people react like that to a challenge. Scott made a good block.”
Balotelli has never strayed far from controversy in his time with the Premier League leaders and has a cult following among City supporters.
However, Redknapp was less than impressed by the suggestion that Balotelli and his eccentricity is merely misunderstood.
“What do you think?” said Redknapp. “A lovable eccentric? What do you think?
“He’s nothing to do with me and it’s up to their manager. I’ve got my own opinions, but I don’t like seeing people kick people in the head.
“It’s not something I understand, how you can back-heel somebody in the head when they are lying on the floor. I don’t understand it.”
Redknapp added that he would not be surprised if the FA act where referee Howard Webb chose not to, and take retrospective action against Balotelli who, having been sent off already this season, would face a four-match suspension if he is handed a red card.
“I don’t know. It’s done. I’m sure they will look at it. They must do, mustn’t they?” he added.
City coach David Platt claimed not to have seen a replay of the incident when he addressed the post-match media conference.
After goals from Samir Nasri and Joleon Lescott appeared to have put City well in control, responses from Jermain Defoe and Gareth Bale capped an incredible period of four goals in nine minutes early in the second half.
The drama continued until the end as, seconds before Balotelli’s penalty decider, Defoe slid in and narrowly missed converting a Bale cross for what would have been a Tottenham winner.