The referee had already penalised the Italian centre-back for pulling down Sergio Ramos inside the area in the 28th minute, which allowed the home side to go 2-1 up.
The result leaves the Italian champions third in Group B, eight points behind Real and two behind second-placed Galatasaray.
"We're upset about the result, but it was a good performance and with a man down in the second half we still caused them problems," he told Sky Sport Italia.
"We have time to recover from this situation, but we have to give our all on the field."
"We should think about ourselves and not the referee," he added. "If you make mistakes like we did, then Real Madrid do not forgive you."
Juve take on Real at the Juventus Stadium on November 5.