The forward, who appeared set to leave during the summer, scored twice at Old Trafford to help David Moyes' me get off to a perfect start in this season's Champions League
The England international opened the scoring at Old Trafford before adding a second after the break, with Robin van Persie and Antonio Valencia also on target for the Red Devils in an exciting 4-2 win.
"It's something I'm really proud of," Rooney told ITV Sport. "Delighted to be playing and scoring and it's a good result - the first game in the Champions League is always important and thankfully we got the victory."
However, the striker reacted angrily when repeatedly questioned as to whether he asked to leave the club during the summer transfer window.
"Listen I'm concentrating on my football, as I've done all summer," he stated.
"I've got my head down, I've worked hard to get myself fit and ready for the season. I'm delighted with the way I've come back, delighted I'm back playing and scoring goals.
"The fans have been brilliant, as I've said all along, the fans here have been fantastic with me and it's great the reception I get here so hopefully I can repay them with performances and goals like tonight."
Rooney could have scored a hat-trick after rounding goalkeeper Bernd Leno but could not find the target from a tight angle and admitted he was undecided as to whether to shoot or pass to strike partner Van Persie.
"I don't know, I was sort of in two minds," he explained. "I didn't know whether to shoot or Robin was there as well so I was in two minds so maybe I should've gone straight for goal but at the end of the day we got the three points which is more important."
Up next for Rooney and United in Group A is a trip to Ukraine on October 2 to take on Shakhtar Donetsk, who opened with a 2-0 win away to Real Sociedad.