The Magpies' head coach felt that it was "imperative" not to lose to the second-bottom Baggies, who remain nine points behind Newcastle after the stalemate in the West Midlands.
United weren't able to get the victory that would have extended the gap between themselves and the bottom three - but they did move above Brighton & Hove Albion with the point.
"We're disappointed that we didn't win, of course, but the important thing - with the week we've had - was not to get beat," Bruce told nufc.co.uk after the final whistle.
"I think you saw that the players gave everything they've got to get something out of the game. That attitude and spirit was pretty evident.
"We lacked a bit of quality at the top end of the pitch, we had some opportunities and took the wrong option, but any team without their three main threats - to be without Allan (Saint-Maximin), Miggy (Almirón) and of course Callum (Wilson) is a big blow to us.
"So we have to find a way, certainly until they're back, of grinding out a few results. We'll take a point and it was imperative we didn't get beat."
The Magpies started brightly and fashioned a couple of early openings without making the most of them, and Bruce explained: "That's the quality and chances I'm talking about, where we picked the wrong option, didn't quite find a pass, should have done better, maybe.
"But in a difficult week I couldn't ask for more in terms of what they gave us in their effort and endeavour.
"It was always going to be difficult - a lot was riding on it, it was an awkward pitch. It certainly wasn't a classic, it certainly wasn't enthralling, but we stuck in there.
"Sam (Allardyce) has very quietly shifted (West Brom) around down here and they've been difficult for anybody to play against, for anybody to beat of late, so we'll take it and move on."
Paul Dummett came in for only his third league start of the season at the Hawthorns and had a solid return as the home side were themselves limited to little in the way of clear-cut chances.
And Bruce said: "He was the biggest pleasing thing. He gave us that vital experience, he was tough and brave.
"We knew we were going to have to deal with their set-pieces on the way to keeping a clean sheet and I'm delighted for Dummy because he's had a difficult period with injury. Let's hope he can stay injury free."
United have now drawn their last two games, and after Friday's visit of Aston Villa they face what could be a crucial fixture at Brighton before the end of the month.
Eleven huge games remain for Newcastle in the 2020/21 season and Bruce insisted: "We have to do whatever we have to do to make sure that we retain our Premier League status, that's for sure.
"There's no doubt we had a terrible run in terms of injuries, illnesses and whatever but I've seen an attitude and a desire that they’re doing everything they can to make sure that we do that."