Sandro limped off in the first half with what Redknapp thinks is a torn calf muscle while Gallas was replaced after the break.
Redknapp's options are already limited by injuries to England stars Aaron Lennon and Scott Parker, while Jake Livermore suffered a facial injury against the Baggies after coming on as Sandro's replacement.
Redknapp said: "Sandro tore a calf - that will be a long one. Gallas as well, it looks like he's done a calf.
"They will have scans tomorrow (Wednesday) and we will have to see how they are."
But Redknapp says the injuries will not affect his plans not to sign any reinforcements in the January transfer window, adding: "I don't have any targets at the moment that I would go to the chairman and say we should get."
Redknapp admitted he was pleased to see his Spurs side come away with victory after conceding they struggled to hit their normal heights.
A solitary second-half strike from Jermain Defoe was enough to settle a drab affair with the visitors' defensive game-plan frustrating Redknapp's men.
The Spurs boss said: "It was a hard game. 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 getting wide and crossing balls which suited them because the centre-halves were dealing with most things and they got bodies back.
"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 and we picked up three big points."
West Brom manager Roy Hodgson hailed Spurs as serious title contenders.
He said: "They have proven that already. There is no question about that.
"They win their matches. They keep putting pressure on Manchester City and Manchester United to win their matches and they are getting some distance between themselves and the chasing pack so they have to be very happy with their first 19 games.
"If they win their game in hand then it will all be a question of seeing which of the three or four teams will have the best last 18 games. The quality is there, the depth of squad is. It's a well-organised club and team. I wouldn't bet against them."