Excitement was in scant supply during a match between two sides stuttering in the league after fine starts but Allardyce was content to see a gritty defensive display from a side missing six regulars.
"We defended really well all the way through," he told Sky Sports. "Apart from a couple of shots from outside the box, which Jussi (Jaaskelainen) has dealt with well, I can't think he's had to make a save.
"On the set plays, particularly in the second half, West Brom had a lot of pressure, put in a lot of good balls, but there was some great defending from our lads.
"We broke well into the final third but didn't find enough quality. When we did, we created a couple of half-chances - I thought Gary O'Neil's effort was in just after half-time - but I'm well satisfied with a 0-0. It's a great point for us under the circumstances.
"(Peter) Odemwingie, (Shane) Long, (Romelu) Lukaku have been very dangerous for West Brom this year and we kept them very quiet; those players haven't had a shot from inside the box.
"It's been a while since we've had a clean sheet and we've had a habit of conceding the first goal in the first half. We've cut that out today, we've tried to win it and it's a tough place to come.
"We've six first-team players out injured so we're down to the bare bones. It was a real good, honest, solid performance from the players."
Allardyce admitted he hopes he will have the chance to strengthen in January.
He added: "We want to push on, we don't want to slip down the league and to do that we'll either have to do a bit in the window or certainly get the players who are injured fit.
"Two or three (injuries), that happens, but six is too many. We coped well today but I'm not sure how long we will cope if we have them out too long."