Song lashed home from 25 yards after five minutes of the Premier League clash at Upton Park, seemingly putting the home side in front against his former club.
However, the linesman deemed Diafra Sakho to be an active player on the edge of the six-yard box and flagged for offside.
Allardyce reacted with bemusement, questioning whether the officials have applied the correct interpretation of the rules, but elected against taking issue with referee Neil Swarbrick at full-time.
"I don't see any real point in confronting a referee after a game when you know you're 100 per cent right and he's only got the visuals of when it happened," he said. "You get nowhere by telling him how wrong he's been in terms of what decision he's given.
"It's more on what we're told at the start of the season and what we're shown - what is an offside and what isn't an offside.
"You base your opinion on your experience and your life as a manager, and you base your opinion on what they tell you.
"What they told us means that they've got it horribly wrong.
"He wasn't in the eye line of the goalkeeper, he didn't touch the ball. Yes, he was in an offside position, but we've seen so many of those allowed as goals and I've never seen one that's actually been not given.
"I'm totally and utterly confused and bewildered."
Arsenal went ahead against the run of play in the 41st minute when Santi Cazorla scored from the spot having been felled by Winston Reid, before Danny Welbeck slid in to double the advantage three minutes later.
Cheikhou Kouyate reduced the deficit nine minutes into the second half, but Allardyce was disappointed to see his side trailing at the break.
"After the first, conceding the second was a bit of a blow, but for me it was a great recovery in the second half," he added.
"I'd like to think that - the way we've been going at home - if we'd been allowed that goal as we should have done, I don't think we'd have lost to Arsenal today.
"Going 1-0 up that early would have kicked the lads on I think and Arsenal would have found life very difficult from there on.
"But it wasn't to be, and sadly we've ended up losing a game that was probably a great spectacle."
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