Two stunning goals from full-back James Tavernier kept alive the Millers' hopes of automatic promotion and all but secured their play-off spot.
"We were magnificent. We showed we have the qualities in the team to be an excellent side," said Millers manager Evans.
"(City boss) Steve Cotterill has signed some excellent players and it is very evident when you see them play, but the only concern we had in the first half is that we should have been four goals up the chances we had. We worked extremely hard.
"But they penetrated us with what was a magnificent strike and if it had got them a point you would have said it was worthy of a point. But Tavernier's second goal was hit with such magnificent force.
"It was the assistant referee who gave the free-kick for the second goal and he was directly in line. We said in the first half two or three times that the goalkeeper was out of his box.
"We are now hanging on to the window ledge with our finger tips for those play offs, but the boys are giving us every chance and I now believe we are just a win away."
Source PA