The Baggies, desperate to get themselves out of the relegation zone, were unlucky score in the match. And speaking after the game, Allardyce was aware of how valuable the point was given the performance of Alan Pardew's men.
"It's a great point for us, there's no doubt about that, given the pressure we were put under by West Brom today," Allardyce told Sky Sports. "The team was resilient enough to hold out.
"There was some brave work from the defenders and goalkeeper when needed, perhaps from West Brom's point of view there was a little bit of sloppy finishing, which is probably why they are where they are.
"But overall I'm pleased with the point and I'm pleased with the performance, certainly defensively with the players we had available to select.
"We had lots of young lads in the side, some experience and lots of players missing that I would have loved to have had the chance to select today.
"The squad has been tested to the limit today and we've managed to get a point.
"In the end, Aaron (Lennon) and Oumar (Niasse) nearly won it for us with the best chance of the game, but it was a battling point rather than a good performance."