Jermain Defoe's second-half strike was enough to keep the club's title challenge on track, as the team struggled to deliver their usual open, attacking, free-flowing football that has become accustomed to Spurs this season.
"It was a hard game," said Redknapp. "It was a tough game tonight. They came - they had lots of injuries as well - but Roy [Hodgson] set them up and they were difficult to break down.
"There were lots of bodies in there and there was nowhere to go. We had the ball for a lot of the game but we were struggling for the breakthrough because they defended well and looked to hit us on the break when they could. They made it very hard for us.
"We created less chances than in any other game this season tonight and the lads were tired, they were leggy. They're not used to playing that many games in such a short space of time - people like Luka [Modric] said he's never felt so tired in there.
"It was hard, if you look at the results over the holiday period you get some funny results, lots of people getting injured, tired legs and it gets more and more difficult to play with the energy and type of pace we normally play with. We were a slower version tonight.
"We were getting wide and crossing balls which suited them because the centre halves were dealing with most things and they got bodies back.
"We picked up a few injuries; I lost Sandro with a torn calf, I lost Gallas with a torn calf, Jake Livermore split his lip open and suddenly we had a very open looking team late on. That's when they started to push and look for an equaliser.
"In the end it was a great win for us, you're not always going to smash teams that come here and play flying football and look fantastic. It was a tough game tonight and we picked up three big points."
Redknapp also took time to praise goalscoring hero Defoe, who made the most of his opportunity back in the starting line-up, turning in a typically committed performance, with his efforts rewarded just after the hour mark.
"He's a goalscorer," the Spurs boss added. "He's turned and managed to get that one in for us and that made all the difference.
"He's a good player, I've signed him everywhere - I signed him as a 14-year-old kid. It's difficult, he has to be patient, but his future is here that's for sure."