Rowett confirmed he had tried to make the tie a test of physique rather than football in an effort to dilute the opposition's Premier League quality.
But Rowett, whose side are eighth in the Championship, said: “We had to try and make the game a bit of a scrap.
“You're hoping a Premier League side with a poor mentality comes, one that doesn't want to be there.
"But what you get with a Chris Wilder side is a team that comes with a brilliant mentality and then the difference comes down to that bit if quality.
“We competed well. But in the end, we just lacked that little bit of quality when it mattered. And they (United) didn't. You saw that."