The 29-year-old England striker came off the bench on 71 minutes and, after being put through by Nani, produced a vintage finish five minutes from time.
"I probably scored the hardest chance I've had," said Owen, who had failed to find the net in United's two opening league games against Birmingham and Burnley. "I had two chances at Burnley and one against Birmingham, but this was the fourth real opportunity I've had.
"I don't think I missed a chance in pre-season, but I've missed a couple since the season started and as ever everyone is quick to write you off. It was as if I hadn't scored for a couple of years.
Owen added: "That's something I've had to deal with for ten odd years now and I don't think that will change until I hang up my boots. It was certainly a great feeling to score. I'd got a few in pre-season but there's nothing quite like doing it in a competitive game."
Owen, who arrived at Old Trafford from relegated Newcastle in the summer, said he believes more goals will come.
"I'd be disappointed if people didn't think I could go on from here," said Owen. "I obviously believe I can as I have done throughout my career and I certainly expect to score more goals in the red shirt."
Strike partner Wayne Rooney
reached another landmark in the victory, firing in his 100th goal for the club as United bounced back in style following their shock 1-0 defeat at promoted Burnley in midweek.
"Of course it's nice to score 100 goals for anyone, especially a team like United, so obviously I'm pleased with that," said Rooney.
"It's something I'll look back on really when I've finished playing. I've still got a lot of games and a lot of goals left in me, so it's not something I'm really too concerned with at the minute."