Keane made a winter transfer deadline-day move back to Spurs after failing to fit the plans of Liverpool, who he had joined only six months earlier.
Benitez has since admitted that the Republic of Ireland international did not suit his strategy and has suggested that the player struggled to cope with the pressure of playing for the Reds.
Keane accepts that he did not match the style of Benitez and is adamant he will not be getting involved in a war of words with the Spaniard.
But the 28-year-old has rubbished suggestions that he could not handle the pressure by insisting his time on Merseyside may have been a success if a different manager was in the hot-seat.
FeudKeane said: "I wish the lads well, Rafa and the staff. I hope they do well.
"I'm not getting into a feud with anyone, I'm too big for that and have too much respect for people and what they do.
"I respect Rafa for how he picks his team and unfortunately I just didn't fit in with how he likes to play football.
"I went there and for whatever reason it didn't work out, simple as that. With a different manager there maybe it could have worked.
"The manager has his own opinions on how he wants to play football and set up a system and I didn't fit with that. But I believe it could have worked under a different manager."