Roma were unable to find a reply to Giorgio Scalvini's 35th-minute goal, and afterwards Mourinho suggested they would have had better luck had Zaniolo not tried to stay on his feet.
"There was a very clear penalty," Mourinho said. "I asked the referee afterwards why, and asked him to be clear with me that it was because Zaniolo did not go down.
"So therefore I have to change my advice to my players, I have to tell them don't try to stay on your feet, don't play the ball, be a clown the way many who dive like they're in a swimming pool do in this league, because that is evidently how you get penalties."
Defeat at the Stadio Olimpico left Roma sixth in the Serie A table, with 13 points from their opening seven games.
"It went badly because we lost a game that we should've won easily, considering the way we played," Mourinho said.
"If we can imagine this domination we had in the final third, with many chances created, we can speculate that with Paulo on the field it might've been different."