New signings Victor Lindelof and Romelu Lukaku joined the Serbian midfielder in making their competitive debuts for Manchester United in their UEFA Super Cup defeat to Real.
United lost 2-1 to the Champions League and La Liga holders but Mourinho remained upbeat after the Skopje clash.
Mourinho, who coached Matic at Chelsea, said of his new £40m defensive midfielder: "I think he played really well.
"I think in the moments where they were moving more the ball, of course it was difficult for us in the midfield.
"But in good moments he was really good and especially in our dominance in the second half after the 2-0.
"In our period of dominance he was what we want him to be - to move the ball in a simple way, to give balance to the team, to start building from the back.
"He is a player with great experience, many years at the highest level and good experience, good stability."
Lindelof, signed from Benfica for £35m, struggled against Zinedine Zidane's superstars while £75m Lukaku had a hit and miss night as well.
The ex-Everton star wasted a glorious chance just after Isco doubled Real's lead but made no mistake with his next opportunity after Keylor Navas parried a Matic drive.
Mourinho said: "It is difficult job to play against a team that dominates the possession - and [Lukaku] tried.
"Of course he missed a chance with an open goal, but he scored his goal.
"He had a good fight against two good central defenders and I am happy with this period and how he fits into - I am never tired to repeat - an amazing group."
