Far from criticising the indiscipline that saw full-back Billy Jones and midfielder Ritchie Towell red-carded in the second half, the Millers boss exuded pride over a battling performance.
Rotherham spent the last quarter of the match with a two-man disadvantage. But it was not until the 86th minute that Adam Webster headed home a Jack Hunt cross to break their resistance.
Warne said: "I am not the sort of manager to contest refereeing decisions. I felt we were the better side 11 against 11 and after the red cards we defended really well.
"We failed to defend one cross into our box. Had it not been for that mistake, my players would have left the pitch feeling like gladiators and it would have been a real lift for the games ahead.
"Every match in the Championship is like a cup final for us. But the spirit is clearly there to lift us up the table.
"I am really proud of what I saw today. We had good first half chances and I was disappointed not to come off at least 1-0 up at the interval.
"The sendings-off changed the game. There are no complaints from me over our performance and we just have to pick ourselves up and go again.
"The biggest compliment I can pay me team, apart from the fact that our fans stayed on at the end to cheer them off, is that the ball went out of play in the 93rd minute and the Bristol supporters didn't want to give it to us."
Rotherham went down to 10 men after 64 minutes when Jones, booked 12 minutes earlier, was shown a second yellow card for pulling back Famara Diedhiou.
Ten became nine after 72 minutes when Towell leapt into a late challenge on Josh Brownhill in the centre of the pitch, earning a straight red from referee Scott Duncan.
The visitors showed tremendous resistance with their two-man disadvantage. But Webster's first goal since signing from Ipswich last summer eventually made the difference as City extended their unbeaten run to seven games.
Home boss Lee Johnson was relieved, but also delighted with the football his team produced in an entertaining game.
"I thought we played really well," he said.
"You have to credit Rotherham for showing tremendous spirit with nine men.
"They made it really difficult for us. But this is a big win because, while we are on a very good unbeaten run, there have been a lot of draws.
"Adam Webster is a brilliant player, as good a central defender as I have had as a manager - and I have had some very good ones.
"He is like a version of Bobby Moore, the way he plays. That might sound outrageous, but the style is similar in terms of touch, sweeping up and reading the game
"I had tried a bit of reverse psychology by telling him he would never score in a million years. Perhaps it worked.
"Derby winning has put us a bit further away from the play-off zone than I had hoped. But we are building something and will keep on chipping away to close the gap."