The pacey winger was taken off on 27 minutes after pulling up following a typical marauding surge down the right flank, and his absence will add further focus on Gareth Bale, who the Spurs boss hopes will return for the midweek London derby.
"Aaron tore a hamstring today so he definitely won't be back for Thursday,” Redknapp told Sky Sports.
"We lost Gareth Bale yesterday evening in training, he's got a bit of a sprain in his ankle, then we lost Aaron Lennon so we lost a lot of pace out of our team and that was a problem.
“Gareth's not too bad; he's just got a sprain of the ankle so we just have to see how he is really.
"Jermain doesn't feel too bad. He's got a minor hamstring tear, he's a quick healer, he could be back in a couple of days."
Roman Pavlyuchenko’s goal arrived on the 61st minute and came courtesy of good work from Rafael van der Vaart, who like the Russian striker, was keen to make an impression on his return to the first team.
Pavlyuchenko’s goal was his first in the league this season and Redknapp spoke of the Russian in glowing terms.
"I'd like to keep him here," he continued. "He's a fantastic player, he's a great striker of the ball and when he's on his game he's top drawer.
"It's just difficult, you've got Rafa, you've got Defoe, you've got Pav and you've got Adebayor and you can't play them all.
"But you need them as was shown today. We lose a couple of strikers and he comes off the bench and wins the game for us."
Reflecting on the match itself, Redknapp admitted that Martin O'Neil's side provided a stern test, and praised the attitude of players to claim the three points to reclaim third spot in the league.
"It was a tough, tough game," he continued. "We had to make lots of changes today."
"No-one is going to be easy. They came here today and set themselves up well Sunderland. They always looked dangerous on the counter-attacks, so it was always going to be a tough game.
"But we stuck at it, and once we scored a good goal from Pav, we pushed on and we made some good chances."
How do you stay up to date with football when on the move? With http://m.goal.com – your best source for mobile coverage of the beautiful game.