That Balotelli scored the injury-time penalty to seal a dramatic victory for the hosts only made matters worse.
The controversial Italian, introduced as a substitute after Tottenham had hauled themselves back from two goals down, got involved in a tangle with Parker during the second half.
His initial contact appeared to be accidental. But a second seemed to involve a deliberate movement of the foot by Balotelli, who has been sent off three times in his short City career already.
TV pundits Graeme Souness and Gary Neville were in no doubt it should have brought a red card from World Cup final referee Howard Webb.
And Redknapp was clearly of the same opinion.
"What reason did he have to backheel Scott in the head with his studs when he is laying on the floor?" said the Spurs chief. "I couldn't see a reason for it. It is not a nice thing to do. It has no place in football.
"Having looked at it, yes, I do (think Balotelli should have been sent off).
"It is not the first time he has done that and I am sure it won't be the last.
"I am the last person to talk about getting people sent off and what they should and shouldn't do.
"But it is blatant. He reacts to challenges like that at times."
The Football Association will wait for Webb's report before deciding what action should be taken.
It was not immediately clear whether Webb saw any of the incident, or none, although if he did not, a suspension seems certain.
It is the latest in a long line of problems involving Balotelli, who seems incapable of staying out of trouble.
"He is not my problem. Let someone else have the problem," said Redknapp.
"He is a good player, of course he is. We all know he is a talent.
"But loveable what? I have my opinions but it is up to their manager.
"It is not something I understand, why he should go and backheel someone in the head when he is on the floor?
"What happens now doesn't interest me. What is done is done. But I am sure they (the FA) will have a look at it. They must do mustn't they."
City manager Roberto Mancini has been embroiled in enough controversy over the last few games for waving imaginary cards.
Under the circumstances, it was probably just as well the Blues chief was unable to attend the normal post-match press conference due to a sore throat, with assistant manager David Platt taking his place.
"That is what has got levelled at me," said Platt of the incident. "I haven't seen the VT. Until I have, I can't comment.
"I never saw anything live. I don't think there was any kind of reaction from the players live either.
"But if someone has seen something, I will be able to comment once I have seen something from a different angle.
"What we are aware of in the last month is that different angles can show different things."
The incident overshadowed a dramatic conclusion to an amazing second half. A cagey opening period gave way to a goal fest.
David Silva sent Samir Nasri through for the opener with a brilliant defence-splitting pass before Joleon Lescott somehow shoved a second over the line from barely a yard.
It seemed a City victory was certain but almost immediately a catastrophic Stefan Savic mistake gifted Jermain Defoe a tap-in and when Gareth Bale found the roof of Joe Hart's net with a staggering strike, Tottenham were level.
Balotelli's introduction - and controversy - came after that but it seemed Tottenham would win when Bale rolled a cross to Defoe in stoppage time, only for the England forward to slide the ball narrowly wide.
Play immediately switched to the other end, where Ledley King upended Balotelli, offering the nerveless striker a chance to seal victory and send City eight points clear of their opponents.
"We have gone up one end and it has looked like we would score the winning goal with Jermain," said Redknapp.
"The goal has come so late. It looked like a penalty.
"It is going to be hard to win the title but all I have ever said is we had a chance.
"We are genuine. There is not much between the teams. We are not a million miles behind Manchester City or anyone else.
"We are a good team in our own right.
"I only said it wasn't impossible. It is difficult now. There are lots of points between us.
"We just have to keep going and see where it takes us."
Mancini was apparently unhappy at the final whistle and lambasted his team for the manner in which they threw away the lead.
"The manager's voice wasn't good but his words in the dressing room were very profound," said Platt.
"Regardless of the fact that it is a great victory against someone who is up there as well, he is not happy at the gift of a goal and the lapse in concentration to allow it to go in.
"He has made that clear in no uncertain terms."
