City number one Shay Given is out of his side's three remaining games after dislocating his shoulder during last week's 0-0 draw against Arsenal.
With Faroe Islands international Gunnar Nielsen the only fit goalkeeper at Eastlands, manager Roberto Mancini applied to the Premier League for an emergency loan and subsequently drafted in Sunderland's Marton Fulop to face Aston Villa on Saturday.
Mancini had been keen to recall England goalkeeper Hart from his loan spell at Birmingham, but the Blues refused and the Premier League would have probably rejected the application anyway, fearing that City would have had an unfair advantage over their rivals.
Redknapp says he does not feel bitter about Mancini's actions, but admits City made a mistake in not including a recall clause in Hart's loan.
"They were talking about getting Hart back but there was no clause in the deal to bring him back," said the 63-year-old, whose side play Bolton at White Hart Lane tomorrow.
"You need to put the clause in the contract if you want him back, if you get injuries that's the key. It was probably an oversight on their part. They should have put it in.
"We haven't complained about it at all, it's no big deal.
"Fulop used to play at Spurs before I came here. The lads here say he was a good goalkeeper. It'll be a tough test for him tomorrow though, Villa are on good form."
Spurs will have Aaron Lennon back as they look to take a big step towards qualifying for next year's Champions League.
They are leading the race to become the first team in five years to break the stranglehold of Manchester United, Chelsea, Arsenal and Liverpool on the top four.
Everton were the last team to achieve that back in 2005, when they edged rivals Liverpool into fifth position.
Redknapp believes it would be a historic achievement if his team could crack the monopoly.
"Breaking the 'big four' would be fantastic for us," he said. "It's important to break that stranglehold, it would be a good achievement.
"They have had it all their own way for a while now."
Redknapp is also understandably proud of having led Spurs from the brink of relegation to the verge of Champions League football since he took over 18 months ago.
"I think we are the most improved team in the league in the last 12 months, without a doubt," he added.
Redknapp will make a late decision on whether to play Ledley King in defence or rest the 29-year-old ahead of Wednesday's crunch game against City.
Meanwhile, Manchester United have been linked with a move for midfielder Luka Modric, but Redknapp insists the Croatian is going nowhere.
"He's not a player we should even be thinking about selling or want to sell," said the former Pompey boss.
"I don't think that will be a problem keeping him here. I don't know what his contract situation is at the club but I'm sure he's happy here.
"He's a fantastic player and I want to keep my best players."