But little does he know ... getting rid of that loser was probably the best moment of last season!
Having left St James' Park 18 months ago for Crystal Palace, the Magpies find themselves on the brink of relegation to the Championship, despite spending £80 million on new arrivals during the summer.
Rafa Benitez has been drafted in to help try and keep the club up, although they could be 10 points adrift of safety before they even kick-off against Swansea this weekend should Norwich beat Sunderland in the early game.
And Nevill, who cited a Daily Mail article by Martin Samuels discussing Newcastle's struggles, is convinced the Magpies' fortunes would be different if his client was still at the helm.
As reported by the Newcastle Chronicle, Neville tweeted: "Perhaps some might realise what a good job Alan Pardew did at Newcastle now."
The comment is likely to generate plenty of debate among Newcastle fans.
But after a bright start Pardew has endured a difficult recent spell at Selhurst Park, with a 1-0 win over Norwich at the weekend his first league victory as Palace boss in 2016.