Although Roma had a good chance through Paulo Dybala early on, Udinese seized control of the game and frequently caused problems for Roma.
Destiny Udogie, on loan from Tottenham, put Udinese ahead, with Lazar Samardzic adding a second.
Roberto Pereyra and Sandi Lovic also scored for the hosts.
Mourinho told DAZN: ‘It was a difficult match. It was a match you could not risk going down, to begin with, because they defend well, they know how to manage the tempo of the game, and they’re physical.
But Udinese… every time they countered either they created a chance or they scored.’
Mourinho refused to criticize the performance of referee Fabio Maresca after the game.
He said: ‘The referee? When you lose 4-0 you don’t talk about the referee. I prefer to lose a game 4-0 rather than four games 1-0. This was ugly, both for us and the fans. But it’s life, and we move on.’
Mourinho was particularly frustrated with the mistakes that his team made, with defender Rick Karsdorp and goalkeeper Rui Patricio among those at fault.
He said: ‘We made mistakes at the worst times of the game. When we got close to 1-1, they practically closed it. They tried everything not to let us play. Now let’s move on, we have 10 points. We are all there, we make our own path.’
Despite the defeat, Roma is in fifth place in Serie A and is just one point behind Serie A leaders, Napoli.
