Bryan Cristante opened the scoring before Mora, Donyell Malen and Evan Ndicka struck in a devastating spell to give Roma a 4-0 half-time lead. Udinese responded after the break through former AS Roma player Nicolò Zaniolo and Palma, but Daniele Ghilardi scored in stoppage time to complete the visitors' victory.
Gian Piero Gasperini was delighted with the quality of Roma's performance, although he warned his players against losing concentration after establishing such a commanding advantage.
"When you play a first half of that quality, there is a risk of deciding the match is already over and dropping your level. I did not want us to make a poor impression here. The first 45 minutes had been too good to spoil," he said.
"The objective was not to concede and to maintain our energy. The first goal we conceded came from a ball that got away from us, while the second was a bad sign that we had switched off. But we also had chances to score another goal and made some poor decisions."
Gasperini was particularly pleased with the variety of Roma's goals and the contribution of his players across the team.
"I recognise all the playing concepts in this Roma side. We scored some beautiful goals. Ndicka scored with a header from a corner, while the others came from excellent assists and equally good finishes. At the moment everyone is confident. There is determination from everybody when we get into those areas. Cristante scores and provides assists, and there is a contribution from everyone."
The coach also praised Ghilardi, whose late goal capped an encouraging performance.
"He was disappointed after the goal that was disallowed in the Champions League. I can see a young player who is responding well. He is in very good physical condition, and in his marking and challenges I can see a player who is developing."
Runjaic, by contrast, described the evening as a difficult one for Udinese, accepting that his side had made Roma's task too straightforward.
"I agree that our approach was very poor. We needed to defend much better for the goals we conceded. It was far too easy for our opponents. Palma also found himself up against a much more experienced opponent and struggled," he said.
"It is difficult to assess the second half. We could have reopened the game, but we did not manage it. It was a black evening for us, and we have to react."
The Udinese coach rejected the suggestion that his team had lacked effort, but admitted they had not shown sufficient maturity.
"Until the first goal, I saw a team that was focused. After that, we were not mature enough. Roma showed a lot of quality on the pitch."
Runjaic insisted he remained calm about his position and believed the squad could recover.
"We have to keep working. We cannot bury our heads in the sand, and there is no point talking too much. We lost the duels today, and that is why we conceded the goals. I remain very clear-headed. I know we can change the situation, but it is not for me to decide whether I am still the right person."