Manuel Pellegrini's Manchester City side have lost four of their last six league games
City crashed to a 4-2 loss after goals from Ashley Young, Marouane Fellaini, Juan Mata and Chris Smalling sealed it for the Reds.
A Sergio Aguero double was the only thing City could cheer on a disappointing afternoon that sees them drop four points off third-place United in the Premier League.
And Neville said after his game he wonders if manager Pellegrini will be allowed the job of restructuring the team for next season.
"There will definitely be change at Manchester City, whether it's the players or the manager,” Neville said on Sky Sports.
“Certainly some of the players. There's some weeds in the garden and you've got to get them out of your changing room pretty quickly. You cannot carry passengers."
City are in danger of losing their Champions League status with current form of just two wins in six games.
They have Southampton breathing down their neck in fifth place, with Liverpool sit sixth - seven points off Pellegrini’s men - with a game in hand.
And there are reports linking former Liverpool manager Rafael Benitez to the City job, while ex-Argentine head Coach Alejandro Sabella has also reportedly been approached.
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