The visitors had the better of a tight first half with Carlton Cole offering a threat to the West Brom goal as the Baggies looked like a side who were on a three-game losing run.
Gary O’Neill came close to breaking the deadlock just after the interval when his curling shot narrowly drifted wide of Boaz Myhill’s right post.
It sparked West Brom into life, and James Morrison was twice denied by the woodwork while Zoltan Gera also came close from a Baggies corner.
“We defended really well today,” Allardyce told Sky Sports.
“Apart from a couple of shots from outside the boxes, there was one really nasty one, but I can’t think of Jussi Jaaskelainen making many saves.
“West Brom had a lot of pressure from set-pieces in the second half and put a lot of good balls in the area but we defended them well.
“We created a couple of half chances – I thought O’Neill’s effort was in – but I am happy with the point given the circumstances.”
He added: “We had six first-team players out injured and we’re down to the bare bones, so it was a good honest performance from the players today.”
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