Red Devils manager Jose Mourinho moved swiftly in the summer transfer window to sign the Sweden international, for an initial £30m, plus another potential £9m in add-ons.
Lindelof was expected to slot straight into United's back four, but having been seldom utilised since the UEFA Super Cup, the Champions League opener against Basel was Lindelof's first taste of playing at Old Trafford.
The 23-year-old told Sky Sports News: "I think it was a very good debut. To play my first match at Old Trafford is something I have really waited for. It felt really good.
"I played my own game and did what I was told to do on the pitch. Now I'm going to leave the match for a while and then watch the replay to see if there's anything that I could have done better.
"I feel pretty confident and know what I'm able to do. [The defensive competition] feels good. They are all good players and I think it's easy to play with them all."