The Premier League second-placed team was beaten 1-3 in snowy, cold Bodø, a Norwegian city located north of the Arctic Circle.
Manchester City's Norwegian star striker Erling Braut Haaland called the team's performance "embarrassing" immediately after the match.
Haaland is part of the captain's group along with Bernardo Silva, Ruben Dias and Rodri, who in a joint statement on Wednesday said they would refund the 374 Manchester City supporters who made it to northern Norway.
"Our supporters mean everything to us. We know the sacrifices our fans make as they travel around the world to support us at home and away and we will never take that for granted," they said in the statement, continuing:
"We understand that there was a lot of travel for the fans who supported us in the cold on a difficult night for us on the pitch. Covering the cost of tickets for our travelling supporters is the least we can do."
