Everton manager David Moyes paid npower League Two side Cheltenham the compliment of playing most of his star performers to clinch a fourth-round visit to Sunderland or Bolton.
Goals from Nikica Jelavic, Leighton Baines, Leon Osman, Seamus Coleman and Marouane Fellaini secured victory, while Yates' Robins managed a consolation effort from Russell Penn.
"We were beaten by a very good side, a very strong side," Yates said. "The scoreline is a little bit harsh on us but they showed the quality they've got.
"Our keeper has made two saves and the ball is in the back of the net five times.
"We can learn a lot from it. We can be proud of our efforts and endeavour to try and play, and we scored a good goal.
"The cup run has given us great exposure and shown we are not a bad side. We kept going, and showed a lot of commitment and quality at times."