Matic featured 35 times in the English league last term, according to WhoScored.com, and he is destined to become a regular at Old Trafford.
"He did well as Chelsea won the league a year ago, but he didn't go back to the level of 2014/15 and Cesc Fabregas was playing a lot more in the second half of last season".
United finished sixth last season but did qualify for the Champions League by winning the Europa League.
United lost 2-1 to the LaLiga giants but Mourinho remained upbeat after the Skopje encounter, picking out Matic in particular for praise.
Conte selected Michy Batshuayi ahead of the striker for Sunday's FA Community Shield defeat against Arsenal, but said that he is happy with his new signing's progress.
Despite having only played 45 minutes for the club in last week's friendly against Sampdoria, the £35million signing impressed throughout the whole match in sweltering Macedonia.
GETTY Man Utd boss Jose Mourinho signed Nemanja Matic from Chelsea for £40m
Chelsea have strengthened too, but not as much as they would have liked given the added demands of Champions League football - but Giggs thinks they will still be in the mix. Was it his dream to go and play for Manchester United? Bakayoko has not and I saw him in the Champions League previous year.
"He seemed like he wanted to leave a year ago at times, although he was very influential and played very well", he said of Costa.
Speaking to Sky Sports News on Tuesday, Neville said: "I said last season that the title will come to Manchester and was badly wrong but I do feel it will be between City and United this time".
"I think in the moments where they were moving more the ball, of course it was hard for us in the midfield". "They've had an outflux, a lot of players have gone but majority were squad players and young players who probably won't affect the first XI that much".
"I'm not sure how good Bakayako is going to be for Chelsea, but he's going to have to be some player to get to the level of Matic".
"They've been very successful over the past 10 to 15 years, so I think you have to have faith in that".
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