Neville was speaking after seeing United beaten 3-0 at home by Bournemouth.
"I don't think he'll get fired," Neville said on NBC Sports after Saturday's result. "I think what I've seen today is what I've seen all season. Three crosses, three goals, the performance levels nowhere near good enough.
"The Newcastle performance and the Bournemouth performance is probably closer to what we've seen all season - rather than the Chelsea performance, which was good in midweek. It's probably a standout because it hasn't happened that much.
"I do feel as if these players need to start taking responsibility, need to start performing better. You look at the goals today, three goals from three crosses, just not acceptable.
"I think we've got to get it out of our head that United have this divine right to challenge for league titles. Look at Newcastle and Aston Villa, they've overtaken United.
"They are a million, million miles from the level that is needed to compete. Where they are at, at this moment in time, is exactly where they should be in terms of the level of performance and quality."