The loss was Mourinho's first at home in Serie A in his career, having been unbeaten for 43 home games during his time at Inter and Roma.
"Compliments to Milan," he said. "I don't want to say anything else, because otherwise I won't be on the touchline next week.
"I am angry at the lack of respect shown to the Roma fans. We did not play well, but we left everything on the pitch. We have that respect, others do not, and that angers me.
"That is all."
The former Chelsea and Manchester United manager then held an equally short news conference, saying: "I made an effort and did not wait for the referee."
Mourinho appeared to be unhappy with the performance of referee Fabio Maresca, who awarded Milan a second-half penalty after he deemed Roger Ibanez to have fouled Zlatan Ibrahimovic.
On the advice of the video assistant referee (VAR), Maresca reviewed the footage at pitchside, but after several views, maintained his original decision and pointed to the spot.
Milan midfielder Franck Kessie scored the penalty to add to Ibrahimovic's first-half free-kick, and it ultimately proved to be the winning goal.
Maresca also sent off star Mila full-back Theo Hernandez in the second half for a second bookable offence but Mourinho's men were unable to get back into the game, despite Stephan El Shaarawy's late strike.
Milan boss Stefano Pioli praised the courage of his team, who moved back level on points with Napoli at the top of the Serie A table after the win.
"We played with character, with our ideas and approach," Pioli said.
"Roma are a quality side, we did very well with 11 against 11, kept trying to score more goals and that is the character we need in such important games.
"We're going through a positive period of form, so we’ve got to ride this wave, be courageous and confident, so I am very happy."