Carragher also accused Alexis Mac Allister of embarrassing behaviour during the match.
The incident that sparked the sharpest reaction came in the second half when Mac Allister tangled with Aston Villa defender Ezri Konsa off the ball, falling to the ground clutching his face after Konsa grabbed his shirt. VAR reviewed the incident for a possible red card before clearing Konsa of any wrongdoing.
Carragher, commentating on Sky Sports, was unsparing.
"He does that every game. Embarrassing. Get him up. I'd be embarrassed if they sent Konsa off for that."
Shortly after the incident Villa made it 3-1, with Ollie Watkins adding a second before John McGinn curled in from outside the box to put the tie beyond doubt. Van Dijk headed a consolation in stoppage time to make it 4-2.
Carragher's broader verdict on the defeat was bleak.
"Far too many weak, physically and mentally players. He's the man that is going to be asked to fix it, Arne Slot. This result does nothing for the feeling of supporters about his position now."
Goals from Morgan Rogers and a Watkins brace had put Villa firmly in control, with Van Dijk's first header the only moment of genuine Liverpool response. The result confirmed fourth place for Unai Emery's side and their Champions League return, and extended Liverpool's miserable run to just three wins in their last nine league games.
Liverpool have now conceded 52 league goals this season — the most by a Reds side in a 38-game campaign. They drop to fifth and need to beat Brentford at Anfield on the final day, while also hoping results elsewhere go their way.