Footage shows the Portuguese teeing off on analyst Giovanni Cerra after a conversation with assistant Rui Faria as United prepared for the Thursday night meeting at Old Trafford.
Midfielder Paul Pogba appeared to be confused after a quick conversation with Mourinho and Faria before the Red Devils boss walked forcefully to the bench to point something out to Cerra.
It is understood that a late change to Zorya's line-up prompted Mourinho to make an alteration himself, which made Pogba unclear on which player he had to mark.
Mourinho said of the bench rant: "It was set-pieces, organisation.
"They changed their team for the game and Paul was a bit confused.
"I want my systems to take care of all the details."
United eventually beat the Ukrainian side 1-0 thanks to Zlatan Ibrahimovic's 69th-minute header to open their winning account for the European season.