After finishing seventh in the Premier League last season, United are embarking on a campaign without European football for the first time since 1989-90.
And Herrera insists Louis van Gaal's squad are determined to ensure they only suffer a single season without continental football.
The Spanish midfielder arrived at Old Trafford from Athletic Bilbao in June, 12 months after first being linked with a move to the Premier League during David Moyes' reign.
Moyes was unable to complete the deal but, when United came calling for a second time, the 25-year-old could not resist the lure of restoring the club to its former glories.
"I would never have left Athletic if it hadn't been for a club like United," Herrera told The Guardian. "United is an opportunity you can't turn down.
"I left a different, unique club, with a special philosophy and incredible people.
"It's a club that few of us have had the privilege of playing for and, who knows, but for United I might have been there 10 years.
"But this is the biggest club in England, a new project, new players and a new coach.
"[There is] desire too: it's been 25 years and the players are conscious of that. They're determined to put United back where it belongs."
Herrera is set to make his Premier League debut against Swansea City at Old Trafford on Saturday.
