Inter beat Genoa 3-1 in Italy's Coppa Italia on Tuesday night, with Adriano getting the game's first goal.
Although the 26-year-old missed a penalty, his display was pleasing for former Chelsea manager Mourinho.
Tottenham manager Harry Redknapp reportedly watched the San Siro match from the stands, with a view to taking Adriano to White Hart Lane on loan for the rest of the season.
"Adriano did his job. He still has to improve his velocity and self-confidence but I'm satisfied with him and the whole team," Mourinho told Inter's website.
"I'm not concerned about the missed penalty.
"We all make mistakes, the important thing is to have the right attitude, desire, respect for the team and the fans.
"If Adriano works like this, a missed penalty means nothing."