Nuneaton were defeated by lower league opponents 3-1, with Town being 3-0 down with an hour gone, writes Tom Feaheny.
While the side can now fully focus on the Vanarama National League North, it still hurt Wright with how they went out.
"It's devastating to be honest, we knew it would be a tricky tie and we knew that they would play football," Wright said to the club's website.
"The big difference was that they were more clinical. We gifted them two goals and we can't afford to do that."
The Nuneaton Town boss said he wanted to say sorry to their supporters after the loss.
"I have told the lads that I feel let down by them and I would like to apologise to the fans that made the journey to support us."
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