The Millers slipped back into the relegation zone after Teemu Pukki's well-taken first-half strike gave the league leaders a deserved three points.
Ben Wiles hit the crossbar and Matt Crooks was denied by a goal-saving tackle as Warne's side chased a leveller after the break, but the boss was honest enough to admit the team he supported as a boy were worthy winners.
And Warne thinks the Millers just came up against the side he thinks will be back in the Premier League next season.
“They are the best team in the league, massive shock they are top of the league and in that sort of form they are going to cause anyone problems,” he said.
"Most managers seem to say Norwich are the best team in this division and I would echo that. There is still a long way to go but I would be amazed if they didn't go straight up - although crazier things have happened.
“But I'm not embarrassed by our performance, I thought the lads competed as well as they could, I just wish we were braver in the press in the first half, that was my only real issue.
“You don't need to gift a team like that a goal the way we did. I thought we were just a bit edgy at the back in the first 10 minutes.
“As the game progressed I thought we grew into it, I am disappointed with the goal that got disallowed, that seemed very harsh.
“We haven't come here for a draw, we came here to try and win. We made attacking subs again to try and get ourselves back in it, our best chance fell to Crooksy and it was a great tackle by their lad to stop a guaranteed goal.
“All in all the best team won, there is no disputing that, but that doesn't detract from the effort the lads put in.”
The Millers' season will not be decided by their result at Carrow Road, instead it will be the home games against teams around them in the table, starting with Nottingham Forest on Tuesday night.