The former Chelsea manager was satisfied with his side's performance at Mapei Stadium but felt they had a traitor in the squad.
Roma returned to league action on Wednesday evening following their 1-0 loss to city rivals Lazio in the Rome derby on Sunday evening.
However, Mourinho's men could only secure a point against Alessio Dionisi's men. Roma dominated the first half, creating the best chance, but Eldor Shomorudov could not beat the goalkeeper after Nicolo Zaniolo played him through.
The second half followed a similar pattern until substitute Tammy Abraham scored in the 80th minute to give Mourinho's side the lead.
It looked like Mourinho's men would run away with the win until Andrea Pinamonti scored five minutes from time to rescue a point for Sassuolo.
But while it is an improvement from Sunday's performance against Lazio, Mourinho is not impressed with the attitude of one of his players, saying he betrayed the team.
Speaking after the match, the Portuguese tactician revealed the player's display betrayed the team's efforts.
"It was a team that wanted to win against a tough opponent, I am sorry that the efforts of the team were betrayed by the attitude of one unprofessional player," Mourinho said. You didn't see me talking that way about Roger Ibanez against Lazio because errors are part of the game. His attitude was never a problem.
"An unprofessional attitude that is not fair to his teammates, that is what disappoints me.
"A point away from home is still not a negative result, and I am happy with the general attitude of my squad."
When pressed on who the player is, Mourinho failed to disclose his name, saying he told him to find another club.
"I won't tell you. I had 16 players on the field tonight, and I liked the attitude of 15 of them," Mourinho continued.
"I told the other that he had this attitude today only and not always. Now we want to close this period of the season with three points.
"In January, he needs to find himself another club," Mourinho concluded.
Mourinho's Roma will round up their campaign for the year when they host Torino on Sunday.