Fourth-placed Spurs are one point ahead of City going into their crucial Champions League decider at Eastlands on Wednesday night.
Victory will guarantee Redknapp's team a place in Europe's top competition next season and go a long way to proving that throwing your financial clout around does not always bring you the success you want.
City owner Sheikh Mansour bin Zayed Al Nahyan has enough cash to turn City into one of Europe's biggest clubs and he will splash more of it around should they claim a Champions League spot.
Redknapp has already experienced the power and wealth of City when the two clubs were involved in a bidding war for striker Craig Bellamy.
"They blow you out of the water," said Redknapp. "We tried to sign Bellamy and, at the time, we were after Wilson Palacios as well.
"They said: 'If you don't drop out of Bellamy, we're going to sign Palacios. We're interested in Palacios. But if you pull out of Bellamy, we'll pull out of Palacios and then we both get a player.'
"They wanted Bellamy badly. It was when Mark Hughes was there, and obviously he was close to Bellamy, The Welsh connection. They were desperate for Bellamy. We were having a bidding war on Bellamy over the fee.
"So we had no choice really. They just said 'We'll blow you out of the water'. They've got the backing, they've got the clout to do that, they can do it if they want somebody."
But whatever the outcome on Wednesday night, and a draw would see both teams take the fight to Sunday's last fixture of the season, Redknapp insists they have exceeded all expectations from the moment he took control of relegation-haunted Spurs in October 2008.
"If we can get in the Champions League next year, it would be great for us," he added. "But if I start thinking about 'Oh I am going to make it' and then you don't make it, you will commit suicide in this game.
"You can't get ahead of yourself. I can't get too up before it happens. Or too low if it does not happen. We have a tough game and need to try and get a result there.
"No one is walking around here thinking 'Cor, we can get in the Champions League' - it has never been mentioned. I have not even spoken to the players about it. We will look at some video of Man City and do our best to win the game.
"We have exceeded expectations definitely. When I took over here I discussed targets with the chairman, it wasn't European football, it was to make sure we did not get relegated.
"We were bottom of the league and chairman Daniel Levy had not slept for a couple of weeks so I helped him sleep by getting us out of trouble.
"I didn't come here saying 'I'll get you into the Champions League, Daniel'.
"But he's sleeping well now, especially with the chance of getting into the Champions League."