A goal with seconds on the clock from Jorge Grant gave the League Two club victory.
Oxford twice came from behind to level and deserved to take County back to Court Place Farm in ten days.
But it wasn’t to be when Grant scored in the final minute of time added on.
Nolan said Oxford were outstanding - and knows his side got lucky.
“I'm very relieved and rightly so because weren't up to scratch today," he said.
"Oxford City came with a great gameplan and stuck to it, which knocked us out of our stride a bit.
"But the resilience, togetherness and camaraderie the lads showed to score a last-minute winner again is absolutely fantastic and great testament to how far they have come in a short space of time.
"We weren't at our normal levels today but we found a way to win, which is always a great trait to have as a team.
"Oxford City were first-class and are very unlucky to be on the losing side. They played us really well and probably deserved more, but that's the drama of the FA Cup."