Spurs have flourished under Redknapp's leadership and are now level with Manchester United and three behind table-topping City after 20 matches.
Their side has been put together for a fraction of the money lavished on Roberto Mancini's squad by the club's mega-rich owners - a fact clearly not lost on Redknapp.
"City are where they are because of Sheikh Mansour and Chelsea thanks to Roman Abramovich," he told The Sun.
"We have not done it that way and it makes me proud. You don't have to go out and spend fortunes to find good players.
"Spurs are not third in the Premier League because someone has walked through the door at White Hart Lane and slapped a bundle of money on my desk.
"City can pay players £200,000 a week, it's unbelievable. The people running Spurs have invested wisely.
"Some of the players we brought in raised eyebrows, like Younes Kaboul, but he's made excellent progress. Hopefully it is coming together now."