Some travelling fans had made over a 1,000 kilometres round trip from Sunderland's home in the northeast to witness the drubbing at the St. Mary's, on the south coast.
Goalkeeper Vito Mannone called on his team mates to reimburse supporters after the abject performance in which he said they had "thrown in the towel" and the squad have confirmed they are happy to oblige.
“We win and lose as a team, players, staff and fans, however we wanted to acknowledge and thank the supporters who travelled such a long way to give us their backing and despite everything, stayed with us until the final whistle," Sunderland captain John O'Shea said in a statement on the club's website (www.safc.com).
Players have offered to refund only the cost of each match ticket, costing 24 pounds, and not the cost of travel for the Sunderland fans that made the trip.
For every fan that does not claim a refund, the squad will donate the cost of the match ticket to a local children's hospice.
Sunderland are 17th in the league with eight points from eight games and host Arsenal in the Premier League on Saturday.
(Reporting By Sam Holden, editing by Pritha Sarkar)
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