The incensed Uruguayans surrounded the referee after the game and, according to Osorio, Gimenez made his feelings known to him as he left the field.
"This behaviour should not be accepted from a professional footballer," the coach said.
"It is impetuous, inappropriate behaviour from a professional who not only plays in one of the best teams in the world -- Atletico Madrid - but also in one of the best national teams in the world.
"I would like to say to Jose Maria Gimenez that any coach has the right to direct the play onto the weaker foot of any player in the world."
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Organisers have yet to say whether they will launch a formal investigation into Osorio's allegations.
Uruguay, who have won this tournament more than any other country, are well known as one of the toughest and most temperamental sides in Latin America.
They had Matias Vecino sent off just before halftime and three other players were booked. Mexico also had a player booked and another sent off.
The result leaves Mexico top of Group C, ahead of Venezuela, who beat Jamaica 1-0 earlier in the night, on goal difference. Uruguay face Venezuela on Thursday while Mexico play Jamaica the same day.
(Writing by Andrew Downie. Edited by Adrian Warner)
