Estudiantes win La Plata derby to go top
Goals by defender Federico Fernandez in the 37th minute and captain Juan Sebastian Veron, with a 45th-minute penalty, gave Estudiantes the win that puts them two points clear at the top after eight matches.
Estudiantes, South American champions last year, have 19 points, Velez Sarfield 17 and San Lorenzo 15 in the top three places.
Gimnasia, one from bottom with five points and only one win, had midfielder Fabian Rinaudo sent off two minutes from time for a second booking.
"We tried everything we could but a change of air is necessary (for Gimnasia) to get out of this situation," Cocca told reporters at the Quilmes ground where Estudiantes have been playing their home games while their stadium is refurbished.
"We'll be urging the team on so they stay in the first division," a visibly downcast Cocca added.
The match went off peacefully with only home fans allowed to buy tickets as a security measure due to the potential for fan violence at the La Plata "clasico".
Cocca is the fourth coach to have lost his job so far this season after Independiente's Daniel Garnero, Antonio Mohamed of Colon and Huracan's Hector Rivoira all departed last week.
At the weekend, Estudiantes are away to San Lorenzo while Gimnasia host struggling title holders Argentinos Juniors.