The Scottish league leaders lost for the first time to Killie at Parkhead in almost six decades on Saturday and Welsh defender Matthews acknowledges it was a very shoddy performance from the reigning champions.
"We just want to apologise to the fans. They shouldn't have to come along and watch that. We're disappointed, not just with the result but the performance," he said.
"We were nowhere near top gear, it was just a bad game. We have to try and do better next time. The manager was very disappointed and let us know."