A solitary Jermain Defoe strike in the second half decided the game, with The Baggies making it difficult for the North London hosts.
Redknapp admitted that his team did not play as well as they have been in recent weeks, but feels the three points is the most important thing.
“It was a hard game,” the Spurs coach admitted to Sky Sports.
“It was a tough game tonight. They came – they had lots of injuries as well – but Roy 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 Wiliam 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,” he concluded.
Spurs have Cheltenham in the FA Cup on Saturday, before entertaining Everton at White Hart Lane next Wednesday.
By Gareth McKnight