Owen joined United on a free transfer this summer and came on as a second half substitute during yesterday's 1-0 victory at home to Birmingham City, but the 29-year-old striker was guilty of wasting a glorious opportunity to score.
The former Liverpool and Newcastle United striker was denied by Birmingham goalkeeper Joe Hart after being released by Wayne Rooney, but O'Shea, who captained United in the absence of Rio Ferdinand, is sure his new team-mate will be amongst the goals in the very near future.
The Ireland international told The Daily Telegraph, "Michael was unlucky with a couple of chances, but I'm sure he'll get off the mark soon.
"I think he'll be like Wayne Rooney in that he'll get his goals in runs. The sooner the first one comes, the better.
"As for Wayne, I think pre-season was so important for him to get that sharpness he needs. Once he gets that, he's so hard to stop.
"His goal against Birmingham will give him a lot of confidence, and it's only going to benefit us in the games to come."