Killie won 2-0 against the Lowland League side last Saturday but brought on Daniel Armstrong for a debut in the 72nd minute despite the midfielder being the subject of a suspension in the competition.
Killie admitted breaching rules at a Scottish Professional Football League disciplinary hearing and East Kilbride were handed a 3-0 victory.
Armstrong picked up his second yellow card in the group stages during Raith's final game in last year's competition, which sparked a one-match ban for the following season.
A Kilmarnock statement read: "As a club we reiterate our apology to our fans, who have supported us magnificently, as well as East Kilbride and the footballing authorities for this inadvertent breach.
"While processes are already in place to try and prevent something of this nature occurring, clearly mistakes can and have occurred in this case.
"After quickly investigating the circumstances, we have immediately added an additional step to our internal procedures to ensure this cannot happen again."
Killie, who were also handed a suspended £5,000 fine, have slumped to the bottom of Group G with East Kilbride moving top.
But the Ayrshire side's Championship rivals, Morton, have also experienced a difficult start to their campaign. A Covid-19 outbreak forced them to forfeit their opener at Stranraer and hampered them in a goalless draw with East Kilbride.
Killie take on Clyde at Broadwood on Saturday in their second game of the group stage. Armstrong will serve his suspension on Saturday.