Spurs are currently fifth in the Premier League two points behind fourth-placed Arsenal with six games to play this season.
Venables said in his column in The Sun: "Do not blame Andre Villas-Boas if Tottenham fail to book a Champions League slot this season.
"The knives will undoubtedly be out for the manager should his Spurs side finish outside the top four. But I think it would be wrong if he carried the can.
"If the Lilywhites' season does end in disaster, fingers should be pointed at the boardroom where chairman Daniel Levy's failure to sign a much-needed striker in January looks as though it could prove costly."
Spurs take on Manchester City on Sunday as their quest for Champions League football continues.