Jermain Defoe's solitary goal was enough for the home side to take three points despite being largely kept at bay by the visitors with Baggies boss Roy Hodgson left frustrated
Jermain Defoe's second-half goal was enough to hand Spurs three points but for the most part they were successfully kept at bay by Roy Hodgson's team.
The win for Tottenham also closes the gap to three points behind second-placed Manchester United, while Spurs sit five points clear of Chelsea who lie in fourth.
"It was a hard game," Redknapp told Sky Sports. "It was a tough game tonight, they have lots of injuries as well but Roy set them up and they were difficult to break down.
"They got bodies in the way and there was nowhere to go when we had the ball for a lot of the game.
"We were struggling to get the breakthrough because they set themselves up, defended well and looked to hit us on the break when they could. They made it very hard for us."
Hodgson declared himself "proud" of his side's display against the Premier League's third place team, and even thought his men looked the more likely to score during the second half.
"I thought we played as well as we could expect to play, that’s for sure," Hodgson said.
"In the first half we allowed them a bit of time on the ball so we were under a bit of pressure, but our defending was good and our shape was good.
"Strangely enough, towards the end of the game we started to show a little more composure and play ourselves and in the end, to some extent, we had them hanging on more than the other way around."
The former Liverpool manager could not hide his frustration, however, as once again he felt West Brom were unfortunate not to come away with a share of the points.
"It’s one of those horrible defeats I’m getting quite used to; there have been many of those in my Fulham and even my Liverpool days," he said.
"We’ve come away with the team having played well and taken no points at the end of it.
"I’m looking for one time when we come here and play unbelievably badly, have an incredible amount of good luck and sneak away from here with a victory, but it hasn’t happened yet."