Bale will on Monday have a scan on the left ankle that he injured against Blackpool, with Redknapp admitting the Welshman could have suffered ligament damage that may require an operation.
"It will take a miracle (to finish fourth)," Redknapp said. "(City manager) Roberto Mancini has got a fantastic squad. They're in a great position. They are six points ahead of us and they have a better goal difference by miles."
Bale's pace and penetration will be hugely missed by the Londoners, who need to win all three of their remaining games against Manchester City, Liverpool, and Birmingham to have any chance of bringing Champions League football to White Hart Lane for a second successive season.
Spurs head to fourth-placed City knowing that only a win will keep them in the hunt for a top-four finish.
Tottenham's current plight is completely different from the turn of the year when they seemed certain to pip their big-spending rivals to fourth position.
Injuries to key players like Bale and Tom Huddlestone, and Rafael van der Vaart's loss of form have all contributed to the club's recent slump, according to Redknapp.
"When we've needed that little bit of magic in the last month or six weeks, Gareth has been injured and we've lost that little spark that turns draws into wins," the Spurs boss added.
"Gareth and Rafa were so good, they were the difference between drawing and losing. They were turning games with fantastic individual performances as well as the team playing well.
"I don't see what will stop them (City). They will keep improving their squad until eventually they will win the championship."
Source: PA
Source: PA