The young full-back was eventually taken off on a stretcher during the 3-2 defeat, leading to a lengthy spell of injury time at the death.
Rushian Hepburn-Murphy was also down for some time before being substituted during a disjointed second half.
The medical department have assessed Reece and he has concussion, but is okay, so the club will follow the standard recovery protocol.
“I think the lad led with his arm and he had a black eye straight away,” lead coach Neil Wood told MUTV. “It knocked him out and the stoppages disrupted it. It happened again with their lad going down and stopped the flow a little bit.