Redknapp, whose team will prevail in the battle to finish fourth and clinch a Champions League play-off spot if they beat City, said the world's richest club warned him off signing the Wales forward from West Ham United in January last year when he was also trying to buy Wilson Palacios from Wigan Athletic.
"We were having a bidding war on Bellamy over the fee. They came in and said: 'You know, if you don't drop out of Bellamy, we'll sign Palacios as well and you won't get any of them'," Redknapp told reporters at the club's training ground.
"So we had no choice, really. They just said: 'We'll blow you out of the water but if you pull out of Bellamy, we'll pull out of Palacios and then we both get a player.'
"Did they want Palacios? Not really, I don't think, no. They were half-interested.
"What can you do? It's difficult. You've got a difficult decision, haven't you? And then, obviously, the money that they offered Bellamy, we couldn't compete with anyway."
The much-travelled Bellamy eventually joined City for 14 million pounds while Honduras midfielder Palacios went to Spurs for about 12 million pounds.
City are owned by Arab billionaire Sheikh Mansour bin Zayed Al Nahyan, whose money has helped purchase internationals such as Carlos Tevez, Gareth Barry and Emmanuel Adebayor.
Asked if City's tactics were acceptable, Redknapp replied: "It's reasonable ... they can do it, can't they? They've got the clout to do that. They can do it if they want somebody."
He also predicted that City, who have already been linked with moves to buy a host of the world's top players for next season, will win the Premier League possibly in 2011.
"With the players that people tell me they're trying to bring in over the summer, they're going to put a team together that could win the championship. They probably will win it.
"If you bring enough world class players in, you're going to have a chance."
Spurs are one point ahead of City with two games left and Redknapp believes the Manchester side are feeling the heat more than the north London club who have already overachieved.
"There's no real pressure on us. We'd have taken this at the start of the season," he said. "For sure, there is more pressure on them. If you had asked me at the start of the season who the top five would be, I'd have put Liverpool in there and City."
Liverpool are seventh after a disappointing season.
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