The travelling faithful endured an 8-2 defeat at Kenilworth Road on the opening day of the 2017/18 season.
Midfielder James Bailey captained the side in Bedfordshire and issued an apology on behalf of the players.
“We know we let ourselves and the fans down,” Bailey told YTFC.net.
“We felt the same as everyone else connected with the club and know the performance was unacceptable.
“The support we had at Luton was fantastic and we didn’t repay them how we wanted. Most were still there at the end of the game when our performance didn’t merit that.
“As a group, we want to apologise and give fans their money back.”
Manager Darren Way suffered his biggest defeat as Town boss and supported the players’ decision to offer a refund.
“Saturday was never going to be easy but the manner of the defeat was totally unacceptable and I apologise to the supporters and take full responsibility for that.
“Paying supporters their money back is a collective decision, we’re not happy with just apologising but at the same time know our best apology will come on the pitch in the coming weeks.”
Information on how supporters can claim a refund from the trip to Luton Town will be released on Monday 7th August. For supporters who watched the Glovers at Kenilworth Road, please retain your matchday ticket.