Matic made his Premier League debut for the Red Devils in last weekend's 4-0 victory over West Ham United at Old Trafford.
The Serbian will experience his first away league match as a United player on Saturday, meanwhile, when the 20-time English champions travel to Wales to take on Paul Clement's Swansea.
"I think Manchester United fans are amazing. I saw Old Trafford and know that they really love the club and support us during 90 minutes. I think away, they're even better. When I played against Manchester, I could feel they are good and always support so I'm looking forward to that game," Matic told Sky Sports News.
Matic signed a three-year contract with United upon his arrival from Chelsea last month.