The Italian club declined to allow Balde to report for national team duty after an invitation for his services from the Senegalese Football Federation arrived late.
Although the Teranga Lions have already qualified for Afcon, Cisse is still ruing the absence of his forward.
"Inter could make the effort to let the boy come,” Cisse was quoted as saying by WiwSport.
“I have club presidents who call me to reach a consensus so that players arrive in camp one day late. We always experience that with the clubs.
“But here it's our fault and we will not hide it. Next time we will try to do better. We tried to convince them to release him, they did not want to. They pointed the regulation saying it was late.”
Caen goalkeeper Seydou Sy has replaced Diallo while Adama Mbengue and Habib Diallo have also been roped in to cover for the injured trio.
Rennes' winger Ismaila Sarr did not train on Wednesday as he recovers from a minor ankle knock though he is expected to be fit for Saturday’s match.