Palace beat Sunderland 4-1 at the Stadium of Light and Carragher feels it was an example of the inconsistencies in Dick Advocaat's side's game.
He says that it is no good putting in good performances in big matches - as they did against Newcastle United - if they do not back it up in the following weeks.
"They're not good enough," he said. "They do it against Newcastle in that big game, but on the back of that you go and lose to Crystal Palace.
"For a club to be continually down there, despite the change of manager and the recruitment of players, they're still a big club. But they are so poor season in, season out."
Sunderland do seem to be perennial relegation strugglers and the lack of progress the club have made in recent times is a concern.
The Black Cats have spent plenty of money on their squad, yet they seem to be devoid of quality, with a number of their players in the twilight of their careers.
It leaves their position in the Premier League looking precarious and only a sizeable improvement will see them claw their way out of trouble.
At the moment Sunderland are just three points above the relegation zone, and with the teams around them starting to pick up form they will be looking nervously over their shoulders.