Manager Jose Mourinho took the blame for the defeat, but also admitted that suffering a single 4-0 loss was a lot better than losing four games 1-0.
The former Chelsea and Manchester United boss got off to a strong start this season with three wins from four games - a run of form which earned Mourinho the Manager of the Month award for September.
However, Roma were simply no match for Udinese as Destiny Udogie, Lazar Samardzic, Roberto Pereyra and Sandi Lovric condemned Mourinho's men to a heavy defeat.
"It was a difficult match," Mourinho told DAZN. "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, they're physical.
"If you go down against them you're already in trouble. We had a good chance at the start with Dybala who was our best player tonight.
"But Udinese… every time they countered either they created a chance or they scored."
When asked about the referee's performance, Mourinho added: "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.
"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.
"I don't have anything more to add. The responsibility is all mine," Mourinho added before leaving the interview. "Udinese were perfect tonight, my compliments to them. We'll be waiting for them in the return game in Rome."