The Salukis, who host Ball State on Saturday, have the worst record in the Missouri Valley Conference. SIU was 14-17 (6-12 in the MVC) during Hinson's first season.
Moccia said he was made aware of Drinkard's tweet, which has since been taken down.
"He's just frustrated like Barry,'' Moccia said. "I can't imagine there will be hard feelings.''
Moccia said SIU fans are used to Hinson's approach and have welcomed him in Carbondale.
"The one thing is Barry has connected with the fans and he has exhibited passion,'' Moccia said. "People are used to his firebrand and bombastic outbursts. That's nothing new for folks around here.
"He does use a lot of colorful language, but people understand. A vast majority of fans like Barry and his passion. He's bringing energy to the program and trying to turn it around."
Jeff Goodman of ESPN.com contributed to this report.