Despite falling behind to an early Jack O'Connell goal and then seeing captain Will Vaulks dismissed for a first-half foul, the visitors prevented Sheffield United from extending their lead until Mark Duffy pounced during the closing stages.
The result, which briefly lifted Chris Wilder's side to second in the table, left Rotherham a point from safety in 22nd place.
Although Warne acknowledged his team must take something from Wednesday's game against Queens Park Rangers to revitalise their push for Championship survival, he said: "Even with 10 men, my lads give us everything. Sheffield United are a really good side and, first-half, I thought we were causing them problems. We just keep ourselves together and then we go again. I'm not dwelling on it."
"My lads never let us down," Warne added. "Obviously the sending off was a turning point. But we looked to hang on and tried to take it to 75 minutes.
"They scored another worldy, to be fair, and that was that. I've had better days but I've had worse. I'm proud to be their manager and I've told them that in the dressing room."
Rotherham, who had held United to a draw at New York Stadium earlier this term, were already facing an uphill struggle following O'Connell's finish when Vaulks received a straight red card for a lunge on George Baldock. The former Falkirk midfielder could have little complaint - he was off the ground and seemingly out of control when he collided with United's wing-back - but Warne later claimed he could have possibly escaped with a caution.
"I haven't seen it back on video," he admitted. "But because Will has given the ball away the ref is probably thinking 'he's going to do whatever to get it back.'
"Knowing Will, he won't have gone in to it looking to hurt the lad. Perhaps I thought it was a strong yellow. But when the ref went to his back pocket, I knew we were in trouble.
"I've not seen it and, if I'm wrong, then I'll apologise. I just thought it was on the edge of harsh."
United, statistically the strongest club on home soil in the division, ended the day in third following Leeds' win over Bristol City. They average 2.17 points per game at their home stadium this season, and last conceded a league goal there on Boxing Day.
With Rotherham facing a punishing end to the campaign, facing leaders Norwich, Derby County, Nottingham Forest and Aston Villa following their return from London, Warne said: "The next two games, I think we need to bring something back on our travels.
"As long as we are in touching distance, I think we'll be okay. We coach the lads well and they try to be the best they can be. We'll go in with a smile on our faces no matter what."
"Sheffield United are one of the best, if not the best, home team in the division," Warne added. "The sending-off isn't an excuse but clearly every team is better with 11 players than 10. Especially us."