Roy Hodgson appointed Neville to a coaching position in May after the former Manchester United defender was acclaimed for his analysis working for Sky Sports.
The appointment has met with scorn by Tevez, who used his column in The Sun to accuse Neville of a conflict of interests.
He wrote: "Spain have been the most successful side in the world for the past few years. Is their assistant manager a TV pundit?
"The short answer is no. Gary has to decide whether England is his absolute focus or does he want to make a name for himself on Sky.
"Because, in my opinion, there is too much of a conflict of interest to do both."
Tevez suggested England's lack of success in international tournaments could be explained by their coaching staff.
"It’s still hard for me to understand why England have not progressed on the international stage," Tevez wrote.
"Players like Steven Gerrard and Wayne Rooney, one of the greatest players I’ve had the privilege to play alongside, possess those qualities — and they’re not alone.
"We’ve got a core of England players at City - Joe Hart, Joleon Lescott, James Milner, Gareth Barry - so I know the class and pedigree is there.
"And it’s difficult to believe the country doesn’t challenge more successfully at the Euros or in the World Cup.
"But maybe England have to look at the structure of its coaching staff.
"Which brings me to Gary Neville. I can’t believe that any of the top countries would employ a television pundit as a part-time coach."
Tevez has feuded with Neville since the Englishman said United were right not to sign him for £25m in 2009.
The pair clashed at a Carling Cup derby in 2010, at which Neville raised his middle finger to Tevez, who responded by calling his rival a "moron" and a "boot-licker" in a radio interview.
- Sports & Recreation
- Gary Neville