Wood put Burnley in front with his fourth goal in as many games and then with the Clarets pressing for a late leveller, Jonny Evans bundled the ball into his own net under pressure from Wood, whose initial effort had been saved by Kasper Schmeichel.
City centre-back Evans looked to have no chance of clearing the ball and went to ground yards after the two players had come together.
But following consultation with the VAR, referee Jon Moss disallowed the goal for a foul by Wood – to the frustration of the striker and his team-mates, whose four-game unbeaten run came to an end with a 2-1 defeat.
“In my opinion it should stand," said Wood to the club's website.
“The ball has bounced off Jonny and gone in and I hear there might have been a little accidental clip of the heels.
“But my eyes are looking at the ball, straight ahead or up, nowhere near him. When the clip happens the ball is already on the line, if not over.
“There is no way he is getting back to clear it and is it clear and obvious enough to overrule the referee?
“In my opinion, no. I don't think that was in the least clear and obvious and it's frustrating.
“I'm a big fan of VAR and it's been brought in for a reason. When it is done right and it is clear and obvious, then ok.
“But in my opinion, if everyone doesn't see it as clear and obvious, them it's not clear and obvious. Hopefully it will keep on improving over the years and we can go on from here."