But he denied qualification for the Champions League would be necessary to keep his top players at the club.
Kyle Walker's spectacular 25-yard free kick sealed victory -- just Spurs' second in 10 league matches -- after Rafael van der Vaart's first half goal sent the home side on their way here on Sunday.
The win lifted Tottenham into fourth place in the table, ahead of Newcastle on goal difference and put them a point in front of Chelsea.
It was all the more the important, coming as it did the day after winger Gareth Bale revealed in a television interview he would have to "sit down and decide what is best for myself" if Spurs failed to qualify for Europe's elite club competition.
The Tottenham boss, speaking before the Football Association announced they had approached West Brom manager Roy Hodgson rather than fans' favourite Redknapp about the vacant England job, said: "Gareth has got to worry about the end of the year but he has a long contract.
"But I don't think he is going anywhere and he won't find too many better clubs than Tottenham.
"This is a great club to be at and you can't be letting Gareth go, he is the future of the club. I think the chairman (Daniel Levy) would want to keep him and we need to keep him."
Fourth place would usually be enough to gain entry to the preliminary qualifying stage of the Champions League, but should Chelsea win this season's competition, only the top three in the Premier League will qualify.
But a win over Bolton on Wednesday would leave Tottenham a point behind third-placed north London rivals Arsenal with two games remaining.
"Finishing third is going to be hard," said Redknapp. "But you never know, it is all to play for. We just have to keep going. I can't see Chelsea losing too many either.
"Newcastle have got some tough fixtures, so we have to keep going and see what happens.
"It was nice to get a win. The only bad performance in recent games I can really put my finger on was Norwich (Spurs lost 2-1 at home to the Canaries on April 9).
"I felt we had been playing well, but the results weren't going our way. But it was good to get back on track again."
While Spurs were wasteful and hit the bar three times in the first half, Rovers were so inept they became the first Premier League side since 2004 to fail to register a single shot at goal.
Van der Vaart opened the scoring in the 22nd minute with his 10th goal of the season, poking home the rebound after Bale's header hit the bar.
Tottenham went off the boil before Walker's 75th-minute free kick, which curled round the Blackburn wall and into the top corner.
Defeat left Blackburn second from bottom in the Premier League and three points from safety.
But Rovers manager Steve Kean remained defiant as he looked ahead to their remaining league games, at home to fellow drop candidates Wigan and away to Chelsea, saying: "It is tough but we need two monumental performances.
"There have been many times this season where people have written us off and we have bounced back," he insisted. "We have to bounce back with two wins."