United are set to finish outside the top two in the league for the third time in four seasons and last won the title in 2003.
"We need to win the Premiership next season and nothing other than that would be acceptable," the defender told reporters on Monday.
"It's got to be now. You can't wait at this club for two or three seasons. Fans won't accept it and the manager won't accept it.
"We've bought a lot of young players and there are a lot of experienced ones and no-one at this place is going to wait one or two seasons for success to come back to us."
Manager Alex Ferguson is building the side at Old Trafford around the likes of Wayne Rooney, Cristiano Ronaldo and Rio Ferdinand.
But United fell behind to Arsenal and champions Chelsea this season in their bid to add to their eight titles since the Premier League began in 1992/93.
"We need success to be now and next season we need to win the Premiership. That's the end of the story," Neville added.
United are 17 points behind Chelsea, who they play at Old Trafford on Tuesday, and six adrift of second-placed Arsenal but Neville believes the gap can be bridged next season.
"I don't think there's much to choose between the quality of ourselves, Arsenal and Chelsea," he said. "Chelsea have been unbelievably consistent, more consistent than ourselves and Arsenal and that's where they have won the league."
