The National League title chasers missed the chance to host Premier League Leicester City after a 4-0 defeat in south Wales.
But the scoreline didn’t tell the full story with Wrexham well in it when defender Luke Young was red carded just 13 minutes in.
Barrow isn’t sure his sending off was just and says playing against a League Two side a man short was just too demanding.
"Obviously a lot revolves around the sending-off," he told the Evening Leader.
"We said we wanted to take the game step by step, but we didn't expect that to happen.
"In fairness we got to half time at 0-0 and when you are in that situation it does give you hope to pinch a result.
"We paid the price for playing the game with 10-men for too long."
Barrow added: "My interpretation was that he got the ball first. That was key.”