Eldor Shomurodov had Roma ahead in the final 20 minutes, but they were pegged back by Manolo Gabbiadini.
Mourinho later said, "In the first half there were difficulties at all levels. The team didn't concentrate to the maximum, it was difficult to catch the highest lines, lost balls, little initiative. Only (Nicolo) Zaniolo played with intensity and responsiveness.
"The second half was better, more intense, more pressing, we changed (Henrikh) Mkhitaryan's position, we created, we scored, we could have scored sooner or later. It's very difficult to play against a team that doesn't want to play, who did well to take their point, but for the game it's our fault for lack of quality and their fault for attitude.
"Sampdoria had possession in their own half, they brought down a lot of players in the build-up phase. They didn't create danger, but they tried to make us stretch and make us lose compactness. They created instability for us, then in the second half we changed positions and attitude."
Mourinho also was confident Tammy Abraham's injury wasn't serious.
He added: "I only saw blood, nothing more. He couldn't walk, in the second half we risked a bit because we lost a substitution. I don't think it's serious, but he's definitely not well."
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