Carragher was highly critical of footballers taking selfies in the changing rooms after games. His comments came immediately after he analysed Arsenal's 2-0 win over Manchester City at the Etihad Stadium.
The former Liverpool defender then mocked the ritual by taking a selfie involving himself, former Manchester United defender Gary Neville and Sky Sports presenter Ed Chamberlain as well as other members of the crew from the programme.
Scholes was in agreement with his former England teammate, and says his former manager at United in Sir Alex Ferguson would not have taken too kindly to it.
He said in his column for the Independent: "In my world the dressing room was sacrosanct. The only time anyone was permitted to take pictures in there was when we had won a trophy. Unless I am wrong, Arsenal only got three points for beating City. It wasn't the European Cup final.
"If you want a measure of how private a place the dressing room was when I was growing up at Manchester United, consider this: even Sir Alex Ferguson would knock before coming into the dressing room at the Cliff, the old training ground. The dressing room is for the players, and the players only. It was a rule respected by all the staff at Old Trafford.
"In my final couple of years at United we had one player, new to the team and young, who posted a picture from the dressing room on Instagram or Twitter.
"I won't embarrass him by naming him because that too would contradict the rules about what stays private. Safe to say, the manager went ballistic and the player never did it again."
The selfie craze is widespread among footballers now with the profile of social media increasing all the time, and there is something of a desire from fans on the internet to see pictures of the players celebrating a win after the game.
It seems that any player with a twitter or an instagram feels the need to post pics of themselves with teammates looking happy at the end of games if the outcome has been favourable.
Carragher and Scholes both played in a very different era, this kind of thing really wasn't around until the very end of their career, and these photos don't appear to be everyone's taste.