Owen struck his 200th goal in English football, but the Reds striker was not in celebratory mood after United dropped league points on the road for the third successive game.
"It's always a tough place to come to, but we created enough chances and dominated most of the game," Owen told ESPN. "They are dangerous in certain situations, but we're disappointed not to get the three points."
On his 200th goal, he added: "Scoring has always been a part of my career, and it's always nice to score goals, but it's tinged with disappointment at not getting the win."
Owen's outlook was shared by the rest of the squad in the dressing room. "We're all frustrated in there because we wanted the win and because of the way the results went this weekend. It was an opportunity to close that gap at the top. It wasn't to be.
"We were helped with a few nice results on Saturday, but when you don't capitalise on it, it leaves a sense of disappointment. We've got to focus on [Sunderland] next week. It's a long season and we've only just started. We're disappointed, but we'll bounce back."