Owen made a substitute appearance in victory over Blackburn Rovers and had one decent chance to add to his goals tally.
"One of the draws of coming to a club like Manchester United is that you are always competing at the top level," he said.
"There were many things that stuck in my mind when I was first asked to come and join the club but one of the big things was the chance to play on big Champions League nights and to play in top Premier League games.
"It has to be everyone's dream to play in games like that. It is difficult to win these competitions but it is obviously our aim to do it and it is exciting to be part of it."
He added: "I don't think it takes a goal for me to play well.
"I was average against Barnsley but scored. I played really well against Bolton and didn't. It just didn't get reflected.
"But that is how my career has gone. It is strange, but I am not particularly bothered about it."