Roma, ninth in Serie A but only four points behind Fiorentina who occupy the final qualification place for next season's Champions League, travel to AC Milan on Sunday.
"The Roma fans are the most incredible I have ever seen, the coach is called Jose Harry Mourinho Potter, and he raises expectations," Mourinho told reporters.
"We are fighting a very difficult battle, but nobody will tell us we can’t fight. Against Milan, we will be there."
Mourinho hit back at critics, labelling himself as the perfect example of professionalism despite his team suffering recent poor results.
Roma have collected five points from their last five league matches and lost 1-0 on Wednesday in the Coppa Italia to city rivals Lazio.
"I do not accept in any way that my professionalism and dignity, my heart for this job, can be questioned," Mourinho said.
"If there is a perfect example of professionalism, it is me. I have never missed one match in over 20 years of my career."
Mourinho said Paulo Dybala (30) would not start against Milan due to an injury suffered by the Argentine forward in the match against Lazio.
"Dybala is a truly special player, who in recent years has played in teams with lots of other special players. We don’t have another with his characteristics," the Portuguese said.
