Caolan Lavery gave United an early lead but the National League high-flyers hit back to secure their passage to the fourth round, where they will play Altrincham.
The game kicked off 45 minutes late as the team bus was stuck in traffic for several hours, and the squad only had brief time to warm up for the match against the Red Dragons.
"I thought we gave a really good account of ourselves considering the preparation troubles we had leading up to the game. I don't think we deserved to lose 3-1, we were well in the match," Nelson said.
"We made mistakes for the goals that they scored and got punished for them.
"It was frustrating to prepare like that but there was nothing we could do about it. At the end of the day, it is what it is. We hit traffic along with plenty of other people on the road, and it did disrupt the preparation but the lads went out and gave a good account of themselves considering.
"They had every excuse you could think of today. For instance, we couldn't get to the hotel for our pre-match meal so the lads hadn't eaten anything since lunchtime, we arrived late at 8pm and kicked off at 8.30pm. They had all the excuses to roll over and get beat comfortably tonight but they didn't do that - they went out, rolled their sleeves up and gave a good account of themselves. I'm pleased with the way they played."
Updating on Reagan Ogle, Marcus Carver and Andrew Boyce's absences from the starting eleven, Nelson said: "Reagan has a thigh issue so we didn't want to risk him. If we'd played him tonight we risked losing him for a number of weeks, so we decided to leave him at home.
"We left Marcus Carver on the bench because he's carrying a groin issue at the minute, so we're trying to protect him.
"Boycey was due to be in the time but he was ill overnight, so we had to leave him at home. We're hoping all three can be involved come Boxing Day (against Chesterfield at home)."
See more from Michael Nelson on Iron Player.
