Alex Song’s early strike appeared to have put the home side in front until referee Neil Swarbrick ruled it out after both Cheikhou Kouyate and Diafra Sakho were judged to be in offside positions.
Allardyce said: “I don’t see any point in confronting the ref when you know you’re 100 percent right and he hasn’t had the visuals. You can’t get anything out of telling him how wrong he’s been.
“It’s more on what we’re told at the start of the season, what we’re shown about what is an offside and what isn’t, so you base your opinions on what they tell you. What they told us means they’ve got it horribly wrong.
“He [Sakho] wasn’t in the eye-line of the keeper. He didn’t touch the ball. Yes, he was offside, but we’ve seen so many of those allowed as goals.
“It’s gone through the legs of Sakho, who is three yards to the right of [Wojciech] Szczesny, so he’s not in his eye-line. There are six players obstructing his eye-line. It’s come through everyone. I’m completely confused and bewildered. There are far too many inconsistencies.”