Spurs have endured a stuttering start to the new Premier League season and sit 9th after 12 games.
They've also only managed nine goals in that time, three of which came from the penalty spot.
That has increased the pressure on the Tottenham boss, who spent more than £100 million seven new players to counter the loss of Gareth Bale.
Villas-Boas claimed before the start of the season that the new arrivals would help Spurs not only break into the top four and claim a Champions League spot, but also challenge for the title.
The defeat at the hands of Manchester City on Sunday marked the third game in a row that Spurs had failed to score, and leaves them eight points adrift of Premier League leaders and rivals Arsenal. Afterwards Villas-Boas said both he and his players should be "ashamed" of their efforts.
According to the Daily Mail, Villas-Boas is under "mounting boardroom pressure" following the result.
The paper also claims that some of the Tottenham players are angry with Villas-Boas's comments after the game, and that tension between the club's board and the manager over the transfer policy has risen.
Spurs broke their transfer record three times over the summer to sign Paulinho, Roberto Soldado and Erik Lamela.
The Mail claim that Villas-Boas is absolving himself of responsibility for some of those signings, while adding that the former Chelsea manager's comments have "broken" a code between him and the players that has put their relationship at breaking point.
They also claim that Tottenham's recent failures have exacerbated the feeling that former boss Harry Redknapp shouldn't have been sacked.
Since replacing Redknapp, Villas-Boas helped Spurs record a record points tally last term while also losing key players such as Ledley King, Luka Modric, Rafael Van der Vaart and Bale in his time at White Hart Lane so far.
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