The Robins were beaten 1-0 at Sixfield Stadium on Wednesday night ahead of the return leg back on their home turf this weekend.
"They were miles better than us tonight," Yates told Sky Sports News. "It's 1-0 and I'm probably the happiest man in the ground right now.
"We defended heroically but we didn't play anywhere near what we're capable of. We had some chances, but I'm happy that it's 1-0."
Cheltenham will look to overturn their first-leg deficit at Whaddon Road on Sunday.