TV replays and still pictures clearly showed that Mexico's Jared Borgetti, under pressure from Crespo, headed past his own goalkeeper Oswaldo Sanchez to give Argentina a 10th minute equaliser in their second-round match.
Argentina, who had gone behind to a Rafael Marquez goal in Leipzig, went on to win 2-1 with a brilliant volley from Maxi Rodriguez in the eighth minute of extra time.
Although Crespo challenged for the ball at an Argentine corner, footage aired on television did not indicate
Markus Siegler, FIFA's director of communications, said on Sunday: "Andy Roxburgh and his people in the TSG have looked at this again and after analysing the footage and still pictures they have decided the goal will be attributed to Crespo who deflected the ball.
"If there is any doubt, the goal will be awarded to the attacker."
In 2002 FIFA awarded a goal scored by Brazil against Costa Rica to Ronaldo even though the ball had clearly been deflected in by defender Luis Marin with the striker not getting the final touch. Brazil won that match 5-2 on their way to the title.