The Three Lions qualified after drawing 2-2 with Montenegro on Friday, but the former Manchester United full back has little hope for tournament success.
"The real issue is that the spine of the team is not good enough, as it stands, to take on Spain, Italy, France or Germany at Euro 2012," he said.
"We're now talking about Rooney possibly missing two games of Euro 2012 when what we should be talking about is the spine of a team that has no mobility and can't keep the ball.
"When I look at it coldly, a team that has John Terry, Gary Cahill, Scott Parker, Gareth Barry, Darren Bent and Rooney in its central positions is nowhere near good enough to take on the major nations such as Spain."
Neville made 85 appearances for his country and 400 for United after making his debut in 1992.