The 3-1 derby defeat to Manchester City at the Etihad Stadium on Sunday saw United slip 12 points behind Pep Guardiola's champion, ESPN reported.
City has won two Premier League titles since United's last success in 2013 and Butt, the club's academy boss after 12 decorated seasons as a player, admits the Citizens have been overtaken in their own city.
"For Manchester United now we have got a challenge on to get back to where we want to be, which is the biggest club in the country, but also in the city," Butt told the Premier League Sports Network event.
"That challenge is there for the owners, the board, the manager and the club in general to be where we want to be. And, to be honest, we have got a challenge on our hands to get there."
Butt lifted the Champions League trophy with United as part of an unprecedented treble in 1999, while City won the playoff final to escape the third tier of English football.
But since the takeover in 2008, City has turned into one of the biggest clubs in Europe and Butt said its transformation on and off the pitch has been "impressive."
"I remember in the local area when the rumors started about them buying a lot of land in the east Manchester area and looking to build this massive complex, like a little mini city within the city, and you don't think it is going to happen," he said.
"Before you know it, it's there and you think 'very impressive.'
"It might not be everyone's cup of tea but you've got to admit it is an impressive place to be. And they are winning things.
"Their next challenge is the European Cup because, until you win the Champions League, you can't really be compared to the best teams in Europe. That's their next challenge."