The 22-year-old made his first start of the season and put in an energetic performance on the left flank, impressing both in defence and in attack.
United secured their place in the knockout stages of the competition thanks to Tuesday night's victory at Old Trafford and Mourinho, who previously criticised Shaw's attitude, was happy with the left-back.
"We confirmed our progression but in the way we wanted to," Mourinho told BT Sport. "We played well and got the result. At half time we were playing well and I was not unhappy. The boys played professionally. Luke Shaw offensively was very good and made a great contribution for the team.
"Shaw had waited for a long time, it is not easy to give an opportunity to a player in matches when we need results. I wanted to make changes, but Luke managed 90 minutes and I told him it is a opportunity to increase his levels."
Prior to the game against CSKA, Shaw had only made two substitute appearances in the EFL Cup this season.