The Robins battled hard against a side 67 places above them in the pyramid, eventually slumping to a 3-0 defeat.
"I thought we were good, we were never going to come here and go toe-to-toe and we tried to keep it tight," he said. "The players can be very proud of it, they're a fantastic bunch to work with. We stood up and managed to defend really well.
"We felt we could have done a little bit better with possession on the counter-attack in the first half.
"But today's about nothing other than being proud of what they achieved. People are starting to notice us and the challenge is to keep going."
Yates was appointed Cheltenham boss in 2009.