For the umpteenth time in a season only eight games old, the colourful Portuguese again clashed with television interviewers even though they were trying to praise Stankovic and the Serie A leaders for their powerful performance.
"You like talking about players, I like talking about the team," Mourinho told Sky amid angry exchanges.
"We have won, that's what is important. It's three points, let's go home. I would swap this 5-0 for five 1-0 wins."
Inter, even hotter favourites for a fifth straight scudetto after Juventus drew 1-1 with Fiorentina, were without main strikers Samuel Eto'o and Diego Milito but blew away fifth-placed Genoa at one of Italy's toughest grounds to visit.
Their play has not always been pleasing on the eye under Mourinho but Stankovic is one player who has notably gained in confidence since the former Chelsea boss arrived in June 2008 and immediately criticised the Serb's form.
Stankovic, equally at home making crunching tackles as he is scoring goals, profited from Genoa keeper Marco Amelia's weak clearance just before halftime to join Esteban Cambiasso, Mario Balotelli, Patrick Vieira and Maicon on the scoresheet.
"I went a bit to my right as I thought he might miskick it. It was perfect," Stankovic said.
Asked to give marks out of 10 for the remarkable goal, he showed his usual modesty.
"I don't know, that's for you guys to decide," said Stankovic.
