The former England international defender made the comments following the Villans’ 5-0 defeat to Arsenal at the Emirates Stadium in the Premier League on Sunday.
It was one of Villa’s worst performances of the season and increased threats of suffering relegation to the Championship at the end of the campaign.
Paul Lambert’s side are currently 16th in the Premier League table with 22 points from 23 matches, just three points above the bottom three.
Carragher was far from impressed with Villa’s performance and asked some key questions of the ambition of the club.
“Today the players haven’t produced,” the 37-year-old told Sky Sports on Sunday. “You could talk about the manager’s tactics, the way he's set his team up and how they’ve done this season – is he positive enough? Is there enough quality on the pitch in terms of the goals they’ve got? Obviously not.
"But it comes back to the top and what’s going on at the club. Is the ambition there to try and get Aston Villa back to where it should be and belongs, which is a top-six, top-eight club?
"I know they had aspirations of breaking into the Champions League under Martin O’Neill, but they were always short. I was playing at the time and they were never quite at the top-four level.
"Will they ever get there, who knows? I don’t think so, but they need to get back to being a team who fight for European qualification year-in, year-out.”
Just a few years ago Villa were fighting for top-six finishes in the Premier League, but now they are struggling to even retain their top-flight status.
Perhaps Villa are not ambitious anymore, perhaps they are happy just to be part of the world’s most popular football league.
There have been investments in the Villa team in years gone by, but they have not been enough to make them a top-four contender.
It is not easy to break into the top four of the Premier League, though. Tottenham Hotspur, who have more resources than Villa, have failed to do so for years.