"I am deeply disappointed to be leaving Aston Villa so soon," Di Matteo told the League Managers Association in a statement.
"My coaching staff and I have worked tirelessly to rebuild the squad and I fully expect the players we have brought in to start delivering results in the weeks and months to come."
Di Matteo's side also lost in the first round of the League Cup to fourth tier Luton Town in August.
"I have seen enough over the opening games of the season to suggest that the team we have built will start converting draws into wins and climb the table towards the play-off places," he added.
Assistant coach Steve Clarke will take charge as caretaker manager during the search for a new boss.
(Reporting by Ian Rodricks in Bengaluru; Editing by Peter Rutherford)
