Lennon had to be substituted in the first half as a result of the problem and Redknapp says the winger has no chance of returning for Thursday's Premier League game against Chelsea.
"Lennon felt the hamstring tear. He's got no chance for Thursday," Redknapp said. "It'll be weeks, if it's a tear."
"We'll see about Bale. He's sprained his ankle. He just did it in training. There's every chance Defoe will be fit."
Redknapp also insisted he wants to keep Roman Pavlyuchenko at the club after his goal proved the difference against Sunderland on Sunday.
Pavlyuchenko, who came on in place of Lennon, has fallen down the pecking order at White Hart Lane and has expressed a desire to move on in the January window.
"He's a fantastic player," Redknapp said. "He's got real talent. He's got great ability, I think. He's got a good left foot, a good right foot and is a great finisher. He's top drawer but he's just been unlucky. He didn't start the season great. He hasn't really shown the form that he's capable of so he's slipped down the pecking order a bit.
"It's difficult. Some people are going to be upset they're not in the team. Today I lost a wide man but I thought I'd change it and if you want someone to score he's always likely to. I want to keep all four (strikers). You need them all."
Meanwhile, new Sunderland boss Martin O'Neill felt his players performed admirably against Spurs despite the defeat.
"I didn't think any player wearing a Sunderland shirt today downed tools," O'Neill said. "I saw an effort. It was a little bit misguided at times, but these are the things we have to rectify. Getting goals is difficult.
"I was disappointed to lose the game but I couldn't ask for much more in terms of effort. There were certainly a lot of things I felt were pretty good about us and we certainly never gave up.
"We were euphoric last week having won the game (against Blackburn), but tasted defeat today against a really fine Tottenham side."
Sunderland suffered an injury scare when Connor Wickham was forced off at half-time, but O'Neill was optimistic about the youngster. "I think Connor's going to be okay," O'Neill said.