Mauricio Pinilla's 40th-minute penalty gave the visitors the lead at the San Siro, but Inter hit back early in the second half through Rolando.
Mazzarri, a regular critic of officials, felt Inter should have been awarded a penalty for a foul on Mauro Icardi.
"I don't talk about referees," he said to Rai Radio.
"It's so obvious, how can I not say it was a penalty. I'm fed up of keeping quiet but I will have to."
The draw was a missed opportunity for Inter, who are fifth in the Serie A and four points behind Fiorentina.
It was a key point for Cagliari as they moved five points clear of the relegation zone, and Mazzarri hailed Diego Lopez's men.
"I must congratulate the 'Sardi' because they played well, they made very courageous decisions," Mazzarri said.
"Against Fiorentina we went ahead but we couldn't do that today. Getting in front is important. It was a particular game that we drew, we created a lot of chances but we couldn't take them.
"Unfortunately today we handled a few situations badly.
"We are all a bit annoyed because today we did everything we could to bring the three points home."
