A 90th-minute winner by Stephen El Shaawary saw Mourinho's men claim a 1-0 win at the Stadio Olimpico.
With the clock ticking down, Mourinho mocked the Monza bench by saying: "You talk a lot and then you cry".
His gestures then drew the referee's attention, earning him a red card in the ninth minute of added time.
As a result, he'll miss the upcoming clash against his former club, Inter Milan.
Speaking to Sky Sports Italia after the match, Mourinho said: "I made some gestures, I said nothing offensive.
MORE ON JOSE MOURINHO
Mourinho savages Papu Gomez with cough syrup jibe as World Cup winner speaks on doping ban
Jose Mourinho calls himself 'daddy' in hilarious Instagram comment on Chelsea reunion
"It was because last season some talented people, but lacking in experience, had some nasty words about us.
"Today the only ones making a show on the touchline and trying to pressure the referee were Monza. I am honest, they are a good team and did not deserve to lose today."
Mourinho was dismissed from the dugout on three occasions last season, against Cremonese, Torino and Atalanta respectively - more than any other player or manager in Italy's top flight last term.
However for Roma, their victory was certainly good news.
Most read in Football
Aston Villa 4-1 West Ham LIVE REACTION: Watkins helps hosts extend excellent home record
Andy Carroll scores 40-yard wonder goal for Amiens as French adventure continues
Man City condemn 'offensive chants' about Sir Bobby Charlton following his sad passing
Ex-Spurs star speaks to furious fans as relegation-threatened Ajax lose again
The win over Monza was their third in a row and takes them to sixth in the table, just three points from third-place Juventus.