The Hammers started the game with three full-backs playing in the back four, then lost James Tomkins to injury, meaning they were robbed of their only fit centre-back, with Guy Demel coming on for him.
Both teams are struggling in the bottom half of the table, but West Ham took an early lead through Joe Cole, only to see two quick-fire goals from Nicolas Anelka before the break earn West Brom a 2-1 half-time lead.
The hosts launched a fightback of their own after the break, with sub Modibo Maiga and skipper Kevin Nolan scoring to put them 3-2 ahead.
But Saido Berahino's angled finish secured a point for the visitors, ensuring caretaker coach Keith Downing has overseen three draws in three games.
Allardyce admitted he was disappointed to only pocket a point from a game he described as 'must win' before kick-off, and he told Sky Sports: "Leading twice at home and not winning is disappointing from my point of view.
"The fact of the matter is that we haven't got the defenders on the field that we need - and that, for me, is the key to why we've not won the game.
"Playing four full-backs across the back four because every centre-back is now injured is a massive blow to us.
"In fairness to the lads they showed magnificent coping skills today. The crowd were on their back, not giving them the support they need - and they turned it around to get the crowd back on their side.
"Maybe there was a little bit of fatigue after having to play two games in 48 hours. People say that's the way it is - but it's not right really, and we cope as best as we can. But that's why we probably saw so many mistakes from both teams - there were some tired legs in the end.
"Neither team were showing the sort of energy they normally can in a game like this, so it left some more open spaces - but also left some room for extra errors.
"To lose James Tomkins and those two goals knocked us back a bit - but it was fantastic fighting spirit from the boys."
Allardyce urged the fans to get behind his troops in coming games, saying: "They've got to understand the players are trying their best - they've had to play two games in 48 hours and we've got our injury problems, with Tomkins going off.
"Booing them is not going to help them or give them encouragement to get back into the game.
"But at the end of the day, they pay their money and they can do what they want - we all understand that.
"I'm just saying that sometimes, when there's a lull in the game, get behind us instead of asking us to get you on the edge of your seats, to help us back in the game and try to win it.
"We did a great job today - every player gave 100 per cent. We nearly got a very important victory, but in the end we got a draw."
Allardyce admits he is trying to bolster his beleaguered backline with the winter window fast approaching, and added: "You've got to find the players and get them in - but it's hard and we've been trying for six weeks now.
"We're still trying to clinch a deal we haven't clinched yet. Life is very difficult and the loss of James Tomkins following the loss of James Collins is a massive blow to us, because with Winston Reid we don't have a centre-half.
"It's a big problem for us that we'll have to cope with until we get the players who are here fit.
"We can bring new players in but that can't happen until January the 2nd or 3rd.
"Fulham is a massive game for us on New Year's Day and these players have got to go out and show that they've got the commitment and energy to get the result we need."