The England midfielder was attacked just hours after Everton’s 4-2 win over Leicester in the Premier League.
Video footage shows Barkley speaking to another man in the venue before the unidentified assailant lands several punches on the 23-year-old.
A statement from Barkley’s solicitor on Monday read: “We can confirm that Ross was the victim of an unprovoked attack by a stranger who approached him on Sunday evening.”
An investigation by Merseyside Police is ongoing.
Carragher urged Barkley to learn from the incident in the future.
“I’ve had a smack myself when I was in town as a young player,” Carragher told Sky Sports.
“What will happen today, Ross’ friends and family will rally around him, so will Everton.
“I hope Ross will look at himself. He hasn’t done anything wrong but you’re in a situation, 22 or 23, you’re not a kid anymore.
“You can’t put yourself in that position. That has to stop.”
Barkley avoided serious injury in the altercation and trained with his Everton teammates on Monday.