The 29-year old defensive midfielder blended seamlessly into Jose Mourinho's side after joining from Chelsea during the close-season and made an immediate impact in their opening three league wins which put United top of the standings.
"At the age of 29 I am an experienced player and at that stage of my career I shouldn’t need too much time to adapt," Matic said as the Serbian national team gathered on Monday for World Cup qualifiers against Moldova and Ireland.
"I knew many of United’s players from before as I’ve played against them quite a few times so I had a pretty good idea what I was walking into.
"The team helped me adapt quickly, they treated me like one of their own in the dressing-room from the very first day. We’ve made a pretty good start in the Premier League but it’s a long season and we will see how it goes."
United, who won a record-extending 20th league title in 2013 in Alex Ferguson's last season as manager, scored 10 goals and conceded none in their opening three wins with Matic efficiently pulling the strings in midfield.
They captured their third Champions League crown in 2008 and won the Premier League in the same season but Matic acknowledged that repeating the feat in Mourinho's second campaign in charge of United would be a tall order.
"Winning the Premier League title will be a tough task not just for us but for everyone because there are five or six realistic contenders," said Matic, who helped Chelsea to two league titles during his two spells with the champions.
"But we all know that Manchester United are expected to win every game. As far as the Champions League is concerned, we’ve had a favourable draw and we are hopeful of still being in the competition in the latter stages.
"The 2-1 UEFA Supercup defeat against Champions League holders Real Madrid was a good test of our credentials to slug it out with Europe's best.
"We were outplayed but that was a one-off while the Champions League is a competition where you face different rivals in every round."
Matic earned instant praise from Mourinho after the match in Skopje, having previously worked with the Portuguese manager at Chelsea.
He remained tight-lipped, however, about his move from Stamford Bridge which prompted many to conclude that Chelsea manager Antonio Conte had made a big mistake by letting him go.
"No comment," Matic replied when asked whether he wanted to leave Chelsea's title-winning side or became a surplus to requirements after Conte signed Tiemoue Bakayoko from French champions Monaco.
United were drawn with Benfica, Basel and CSKA Moscow in the Champions League group stage.
(Editing by Ed Osmond)
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