The Scotland international keeper is expected to be sidelined until February with the shoulder injury he sustained after being caught by Defoe during the Black Cats 2-0 defeat at White Hart Lane earlier this month.
"It was a funny one, the ball got played through and I thought I could get a toe in. There was no intention to hurt him," Defoe has told Sky Sports News.
"I talked to Darren Bent, to text him and apologise and he did that.
"I think he's out for a couple of months so, if he's watching, I'm sorry.
"He knows that isn't my game."