Owen found the target in the 59th minute of the 2-0 win with a clinical finish at Oakwell following a ball from Fabio.
Danny Welbeck had earlier put United in the driving seat after five minutes when he headed home a corner from Anderson.
Owen said: "A start and a goal, you can't ask for more than that. It is how people judge me unfortunately.
"I started a game against Bolton and was pretty pleased and thought I played pretty well. Then I looked at the papers and was given a three or four.
"But in this game I played pretty average and scored a goal and I'll probably get seven out of 10.
"I think I deserved a five in this game and seven or eight from the Bolton game."
Manager Sir Alex Ferguson said: "It was a fantastic goal, he had such quick feet, it was a marvellous finish."