The Ivorians needed a win to stand any chance of making the semi-finals, but were unable to find a way past their Malian visitors, who remain in with a chance of qualifying from Group A.
ASEC withstood periods of sustained pressure in the first half as goalkeeper Badra Ali Sangare came to their rescue on more than one occasion.
The home side stepped up the pace after the interval, but wayward efforts from Yako Ablakor and Mark Sekyere cost them dearly, while a deflection denied Hugues Zagbayou late on.
The point leaves Bamako three points adrift of AC Leopards, whom they could edge on goal difference depending on results in the last round of fixtures.
AC Leopards' 4-0 win over Coton Sport on Saturday saw them strengthen their position in second, while their opponents are assured of a place in the last four following Sunday's result.
