Cahill limped out of the action after the challenge on the hour mark and skipper Jamie - booked for the tackle - admitted the incident took the gloss off our fine 1-0 victory.
"It was just not meant," said Jamie, who went to see Cahill immediately after emerging from our dressing room after the game.
"There was no intention there whatsoever and, for me personally, it's taken the gloss off what was a great result for Tottenham.
"I tried to let the ball run and I can imagine it looks bad. As I tried to let it run my left foot has gone out and I don't even try to tackle with my left foot, I'm right footed.
"It was one of those things and I hope there is no serious damage. It's just not my game. I've not been on the receiving end of too many bad tackles luckily enough in my career and I wouldn't wish it on anyone.
"I just hope he's okay. There was absolutely no maliciousness in the tackle, that's all I can say. I can put my hand on my heart and say that."
Jamie Redknapp moved quickly to apologise to Tim Cahill after his tackle on the Everton midfielder in Saturday's win at Goodison Park.