Bryan Mbeumo scored the only goal of the game as the Bees made it two wins in a week and cemented their push for third spot.
The Millers’ defeat puts the relegation fight back in Derby’s hands, and Warne admitted: “The lads are exhausted, the schedule has caught up with us but we will keep going. On another day we might have nicked one at the end.
“It is absolutely exhausting and I don’t know how the players players are doing it.
“We have a small squad and I’m exhausted myself. It feels like we’ve played a quarter of a season in a month and the sad thing is, if you are winning every week you feel a million dollars but when you lose you lick your wounds and they get deeper.”
Warne bemoaned his side’s lack of fortune, with a Covid outbreak, injuries and sending-offs stretching his squad to the limit.
But he stressed: “Unfortunately we are at the stage of the season where if it was the start we’d have been proud, but because we are desperate for points to stay in the Championship, it’s bittersweet.
“It means a lot that people are rooting for us because people don’t root for bad people. We’ve had a few injustices, but they are inspiring the lads to go on and that’s what is keeping them going. I can’t knock the lads’ effort and I was very proud of them.”
Warne said the run-in was “brutal” and added: “We’ve had games recently where we’ve been excellent and should have come away with points. I feel for my group and myself that we haven’t got just rewards, but we will go to the end.”
The Bees took the lead just before the half hour, Sergi Canos cutting in from the left and whipping in a teasing cross that Mbeumo deftly glanced home with his head from 12 yards.
The Millers looked the brighter of the two sides early on and Jamie Lindsay was unfortunate to see his curling drive deflected into the arms of Brentford keeper David Raya.
Rotherham defender Richard Wood saw a header drift just wide of the post from a pinpoint Ryan Giles free-kick before Angus MacDonald blazed a volley over from the edge of the box.
Rotherham’s response to going behind was almost instant, Michael Smith whipping in a cross from the left that eluded everyone but former Brentford man Chiedozie Ogbene but he could only head straight at Raya.
Ivan Toney thrashed a long-range effort wide before beating the offside trap only to fire against the post.
Rotherham, who have now lost five on the trot, almost levelled late on but Michael Ihiekwe’s header was held by Raya.
Brentford: Raya, Goode, Sorensen, Pinnock, Roerslev, Ghoddos (Forss 74), Janelt (Jensen 89), Canos (Fosu 74), Marcondes, Toney, Mbeumo (Bidstrup 74). Unused substitutes: Norgaard, Reid, Daniels, Stevens, Gordon.
Rotherham: Blackman, Ihiekwe, Wood (Ladapo 67), A MacDonald, Harding (Hirst 76), Wing, Wiles (Sadlier 85), Giles, Lindsay (Barlaser 76), Ogbene (Olosunde 76), Smith. Unused substitutes: S MacDonald, Clarke, Jozefzoon, Vickers.
Referee: M Salisbury (Lancashire).