Nada was sent off for kicking striker Yang Xu in the groin after 36 minutes in their opening Group A match. The incident was the turning point in the game, and without him Kuwait were exposed at the back and lost 2-0.
An angry Tufegdzic said the punishment did not fit the crime.
"Yesterday I saw a letter that said he had been banned for one match, now I have just been informed he has a two-match punishment, and I don't understand why," the Serbian told reporters in his media conference ahead of Wednesday's match against Uzbekistan.
"He made a mistake, but he does not deserve to miss two matches."
Tournament Director Tokuaki Suzuki said the extra match ban was imposed because of the serious nature of the incident.
Suzuki also said South Korean defender Kwak Tae-hwi, who was sent off in Monday's 2-1 win over Bahrain, would be automatically suspended for one match.
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