The South African side trailed 2-1 from the first leg of the play-off round tie and were unable to turn things around in Abidjan.
With the Chiefs chasing glory on two fronts domestically, head coach Stuart Baxter remained at home to prepare for his side's next league match, leaving assistant Doctor Khumalo in charge of a squad containing only 13 players on Sunday.
ASEC took full advantage with a 1-0 second-leg win, secured by a close-range strike from Foba Stevens Koffi with 14 minutes remaining.
Etoile Sahel, Confederation Cup winners in 2006, are through to the group stage following a dramatic 1-0 win home win over Horoya.
The first leg in Guinea had ended goalless, but Hamza Lahmar settled the tie in the Tunisian's outfit's favour with a strike six minutes from time.
Last season's CAF Champions League semi-finalists Cotonsport made it past Petro de Luanda 4-3 on aggregate following a 2-2 draw in Angola.
CA Bizertin of Tunisia reached the last four of last year's Confederation Cup, but will not feature in the group stage this time after going out to Zambian side Nkana on away goals.
Following a goalless draw in the first leg, an 80th-minute penalty from Derrick Mwansa secured progression for Nkana, cancelling out the Billy Mwanza own goal that had given Bizertin the lead.
AC Leopards beat Medeama 5-4 on penalties to secure their qualification.
The Congolese side recovered their composure after Medeama had erased a 2-0 first-leg deficit to level the tie on aggregate with two late goals.
Elsewhere, Real Bamako progressed 2-1 on aggregate from the all-Malian tie with Djoliba after a goalless second leg.
