Villas-Boas was dismissed by the club Monday following a 5-0 defeat to Liverpool at White Hart Lane a day earlier, with Spurs seventh in the Premier League.
And QPR manager Redknapp believes Villas-Boas' player recruitment, following the sale of Gareth Bale to Real Madrid in September, has ultimately cost him his job.
"You can't blame the club, with the amount of money they've spent on players," he said. "Unfortunately [Villas-Boas] bought a lot of players in that haven't improved the team. Whether he bought them or the sporting director did, who knows what goes on. They haven't improved the team enough. But they still have enough quality to finish in the top four."
Redknapp, who spent four years at the club and reached the quarterfinals of the Champions League, has been linked with a return to White Hart Lane. However, he dismissed the speculation, and urged the Tottenham board to consider caretaker boss Tim Sherwood.
On a potential return, he added: "That's not going to happen. I had a great time but I've got a great job [at QPR]. I'm working for good people here at QPR. I'm enjoying my time here, we're top of the league and things are going well.
"If [Sherwood) had a foreign name or a more sexy name perhaps he might get that job. I hope they don't think they've got to get someone who's Italian or Dutch or French or whatever. Let's hope Tim can get the job."