Shaw, who has made just two substitute appearances for Manchester United in the EFL Cup this term, was given a rare start in the Champions League this evening.
The England international is widely expected to leave Old Trafford in January, as he seeks to bolster his chances of getting a call-up to the World Cup.
After falling behind to a Vitinho strike on the stroke of half-time, United rallied behind to win 2-1 thanks to strikes from Romelu Lukaku and Marcus Rashford to ensure they qualified from Group A as winners.
McCoist was pleased with how Shaw handled himself, and reckons he sent a timely reminder to Jose Mourinho.
“I thought Luke Shaw was excellent,” McCoist told BBC Sport.
“I was delighted for him and you could feel Old Trafford willing him to do well.
“Shaw invited Moscow to take him on, such was his confidence and pace to see off (Mario) Fernandes.
“He took the ball off him and came up field with pace.
“His link-up play with with Juan Mata was the highlight of the game.
“Shaw came here with a point to prove and he passed it with flying colours.
“United have some great strength and pace and Shaw was a big part of that today.”
United turn their attentions back to the Premier League on Sunday when they face Manchester City (4.30pm).