The midfielder, who missed his new team's first two matches in the Clausura championship due to work permit problems, earned a second booking and a sending off when the referee ruled he had dived in the 84th minute of Sunday's 1-1 draw at the Omnilife.
The red card left Cruz Azul with nine men, defender Gerardo Flores having been sent off three minutes earlier, but the Chivas were unable to take advantage and had to settle for one point at the end of a second half dominated by the visitors.
"I don't think either sending off was deserved, so we were harmed. The team fought, but against the referee it gets very difficult," coach Memo Vazquez, whose side earned six yellow and two red cards to none for Guadalajara, told the club's website.
Javier Orozco put Cruz Azul ahead and Mexico striker Rafael Marquez Lugo marked his return from a two-month injury layoff with the equaliser in the first half.
Colombia striker Teofilo Gutierrez, who like Bertolo fell foul of Mexico's new immigration rules, also made his belated debut in the second half.
The pair, signed before the championship started earlier this month having entered the country on visitors' visas as foreign players had done in the past, had to leave Mexico last week to apply for their work permits at a consulate in neighbouring Guatemala.
Cruz Azul were among several clubs unaware their new signings would be affected by a Mexican government rule introduced in November whereby foreigners coming into the country to work need to arrive with their work permit already in hand rather than make their application once in Mexico.
The Blue Machine, as Cruz Azul are known, are fourth with five points after three matches, four points behind the leading trio of America, Tigres UANL and title holders Tijuana, who won their first ever championship in the Apertura in December.
Guadalajara, rebuilding after the failure of their flirtation with the consultancy of Dutch great Johan Cruyff, have two points.