Wayne Rooney dominated the scoreline with a hat-trick as United proved a class apart.
Schmid told the Seattle Times: "It was 1-0 at halftime. Were they 6-0 better than us in the second half? Yeah, they were because they finished their chances and we didn't finish ours. I felt we had an equal amount of good chances but that's the difference in the quality in the level of play - the ability to finish.
"I need to apologize to our fans because I thought we embarrassed ourselves in the second half, not to take anything away from Man United because they're a great team. They scored some great goals and their movement was superb. We wanted to reward all the guys on the team, wanted to play everybody. I think in retrospect that was a mistake.
"I should have played guys and brought some guys off the bench and not tried to get everybody in the game. We've had a hard season. We've worked very hard and played very well and I wanted to reward all the guys with the opportunity to get on the field against Man United. Unfortunately they didn't reward themselves."
Schmid added: "For me, I know it's my most embarrassing loss, personally. It's not to take anything away because they're an unbelievably good team."