The Belgium international came on for Anderson for the final half hour at Old Trafford and is hoping to start at home to Bayer Leverkusen in the Champions League on Tuesday evening.
Fellaini said: "I was happy with my first 30 minutes. I've tried to do my job - winning duels, clearing balls, playing clean.
"I hope to start in the Champions League. It will be my first experience in that competition and I'm looking forward to it.
"But, the coach decides. It's important we make a good start."
Fellaini also commented on the special reception the fans gave him during the game.
Fellaini added: "It was a nice experience with the fans. They all supported me and I felt confident.
"There were fans with wigs in the stands which is always nice. I want to give everything for this club, for the team-mates and fans. In all things, you feel this is one of the biggest clubs in the world."