Keith Lowe opened the scoring just seconds into the match and Chris Zebroski continued his recent goalscoring form with another striker but Rotherham scored four times to end the Robins' four game unbeaten run.
"We had to chase the game," Yates said. "We needed to stand up because we knew there would be a backlash from Rotherham. It was far from pleasing, but the good thing is we have another game on Tuesday.
"There was a lot I wasn't happy with today. There weren't too many positives to come out of the game. Keith Lowe was outstanding but apart from that I don't think too many got any positives out of the game and that's disappointing.
"The subs came on and livened it up but we knew we had to stand up and be counted and today we didn't in aspects we are quite good at and pride ourselves in.
"We played some decent football but if you give teams goals and look wide open you are going to get caught. It was far from pleasing."