Shaw was handed a rare start in the Champions League clash, featuring in the United starting 11 for the first time in 219 days.
The England international grasped the opportunity with both hands, putting in an energetic performance that left his manager delighted come full-time.
'Some of the guys who do not play regularly, Luke Shaw, especially offensively was very, very good, and made a great contribution to the team,' Mourinho told 'BT Sport' following the final whistle.
'He was waiting for quite a long time, he has been deserving for quite a long time. It is not easy to give an opportunity to a player that does not play for many months in matches where the team really needs results.
'He managed to stay on for 90 minutes. I told him this is not a test, this is an opportunity to play and prove your level. Honestly I am happy with his performance.'
The Portuguese has previously criticised the former Southampton man for his lack of fitness, amongst other things, but there may just be a light at the end of the tunnel for the 22-year-old.