Trapattoni, one of Italy's most successful coaches who returned at the start of the season after an indifferent spell in Germany at Bayern Munich, quit after his club were thrashed 4-1 by the champions, Juventus, on Sunday.
The former Serie A winning Inter and Juventus coach, whose job had been increasingly seen at risk, told reporters at the club he had offered to go on a previous occasion.
"Nothing happened, there was not the reaction I expected. So I have decided to hand in my resignation," he said.
The club said Adriano Bardin, Cagliari's goalkeeping coach, took charge of yesterday's regular training session.
Sunday's defeat was their fourth consecutive away defeat after 4-0 losses to Internazionale, Parma and Lazio.Reuse content