The Red Devils began their Champions League campaign with a comfortable win on the road, thanks largely to two goals and an assist from stand-in skipper Pogba.
However, Mourinho was also keen to point out the contributions of full-backs Shaw and Diogo Dalot, the latter of whom played the full 90 minutes on his debut for the club.
"[Pogba] felt tired in the last part of the game but it was a good performance. Solid, class and gave the team the pace we needed at times," Mourinho told BT Sport after the match.
"He controlled the tempo and of course it was a very good goal. The penalty showed personality too as sometimes when you miss one you have doubts but none for him.
"Both full-backs were very, very good. Very offensive and always eyes open. Very calm. Luke has been doing it since the start of the season and Diogo is one of the best young right-backs in Europe already. He is just 19 years old."
United's win leaves them top of Group H after one game, level on points with Juventus.