Keane returned to Tottenham this week after just six months at Liverpool.
Venables said in his column in the Sun: “I fear Rafa Benitez may have cut off his nose to spite his face by deciding to sell Robbie Keane back to Tottenham.
“I wonder if Rafa let him go because he became fed up with him moaning about not playing.
“Yet dealing with players who are not in the team is when managers earn their money. You have to be able to cater for all your players, even the ones not in the side.
“You cannot just sell them when they are unhappy or every player not in the team will be banging on your door asking for a move.
“It does not matter if Rafa found Robbie hard to handle. He should have kept him until the end of the season at least. Even if it meant upsetting the player by leaving him on the bench.”
He continued: “I am worried Rafa let that earache get to him, when he needed to stay focused on the bigger picture and the part Robbie could play in helping Liverpool win their first Premier League title — and first top-flight crown for 19 years.
“Surely that is worth any amount of moaning from any player. But selling Robbie, with nobody to replace him, was a huge risk. And that decision appeared to backfire when Steven Gerrard hobbled off injured at Goodison Park on Wednesday.
“By selling Robbie, though, Rafa has backed himself into a corner. If Liverpool do not win the title, people will say it was because he sold Robbie.
“The deal was done at the last minute. Rafa had no time to get a replacement in and I am surprised he acted so recklessly, as normally he is so cautious during matches.”
