Andrea Ranocchia put the champions ahead after seven minutes when Houssine Kharja’s shot deflected off the defender and into the net.
However television replays showed that Ranocchia was in an offside position and Donadoni was not pleased with the referee’s decision.
"There's nothing to discuss," he told Sky Sport Italia after the game. "My complaints won't change the result tonight.
"I am proud of my players and can't blame them for their efforts this evening. We improved in the second half and showed some belief," he concluded.
Cagliari have not defeated Inter at San Siro since 1995.