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.
"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."
