Montreal earlier listed a back injury to explain his omission but reports of discord were confirmed after the match.
"I spoke with him (Saturday) and he didn't accept the fact that he would come off the bench and, in the end, he didn't want to be in the 18,” Biello told reporters.
“He decided not to play.”
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Drogba, 38, has been used as a substitute in two of the Impact’s last four games.
He was recruited from English Premier League club Chelsea last July and wasted little time living up to expectations, scoring 11 goals in as many regular season games.
His output has been down this season but he has still managed 10 goals from 18 starting appearances.
(Writing by Jahmal Corner in Los Angeles; Editing by Ian Ransom)
