Sunderland boss Paolo di Canio felt they were robbed of at least a point after defeat to Arsenal.
With his team 2-1 down, Jozy Altidore had a goal disallowed after ref Martin Atkinson blew for an earlier foul.
Di Canio, who was sent to the stands after complaining to the official about Giroud's dawdle from the pitch when he was substituted in injury time, said: "It was a mistake.
"The referee has the power to wait to see how the action finishes, and then he can come back to his decision.
"They have to wait. It's not Paolo Di Canio, it's the rule, so he made a mistake because he stopped the game early, especially in the balance of the action.
"You could see Altidore is much more powerful than Sagna, he was shielding the ball well. It was clear he was near to winning the challenge.
"That was a key moment because we can't imagine that we would have many more opportunities to score, so that decided the outcome of the game.
"That can happen. He is a man. It's important that he accepts this - I make mistakes every single moment when I make decisions with my players; my players make mistakes in front of goal."
