Allardyce lamented both his team's defending and a decision by referee Craig Pawson that had left him "baffled" after the Hammers fell to a 3-1 defeat at Stoke.
"I think in the cold light of day, we have to blame ourselves," Allardyce said.
"But there is a big part to blame the referee for as well.
"There is absolutely no doubt about that in my mind - I have just reviewed the situation on the laptop and watched a blatant handball that stops Andy Carroll chesting the ball down and maybe having a chance to shoot and score a goal.
"It is arm to ball, not ball to arm, and the referee is in a fantastic position to see it.
"So I am totally and utterly baffled by that decision.
"But the other thing is that it is really our fault for the poor defending we showed in the second half - on two occasions, where we just had to defend correctly, and when we were in the ascendancy, particularly with the first goal (Arnautovic's).
"We were in control, and it was looking like if anyone was going to score at that stage, it would be us.
"But then we fall asleep, and I just don't know where our defending went then.
"So those two bits - one from the referee and one from our defence - is why we are not here with some points on the board."
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