The Gunners beat the Eagles in the Carabao Cup quarter-final in midweek after a sensational maiden hat-trick from Gabriel Jesus.
Jesus continued from where he left off. He bagged two goals in the opening half while also providing an assist for Kai Havertz.
Arsenal went into the break with a 3-1 scoreline. They controlled the second half before securing a comfortable victory in the end.
Speaking after the game, Carragher said that a 5-1 away win is a good result and certainly against a Palace side in decent form.
He said: "5-1 away from home at any ground is a good result but certainly against this Crystal Palace team and the run they are on."
With the win, Arsenal have moved within one point of second-placed Chelsea while they are three behind table-toppers Liverpool.
However, the Blues have a game in hand over the Gunners while the Reds have played two games less than the north London giants.