After victory over Los Che on Saturday, Mourinho chose to take the post-match media conference first - when it is traditional for the visiting team to lead the after game questions.
Emery was stunned by Mourinho's behaviour and made it clear: "You want respect from everyone, but when you go to the press conference after the home coach, this is a sign of disrespect.
"You can be a very good coach, but you must have human values and comply with your opponent. I shook hands and congratulated him, but we do not feel respected when we come to play here.
"I do not know if he was in a hurry but it is the first time this has happened and I hope it is the last."