After seven straight wins, Rotherham were sunk by a 66th-minute goal from Stephen Humphrys.
“The lads have been on an amazing run,” said Warne of his fourth-placed side.
“The lads are disappointed to lose, but I think we came up against an excellent team. I think their position in the league doesn’t say how good they are, really.
“We got a little bit run-over in the middle of the park. We may well have rode our luck in recent weeks, I’m well aware of that, and (on Saturday) we probably didn’t have that.
“I don’t think everyone was on song. We just didn’t get our passing game going. We didn’t get wide enough, quick enough. We came against a really good team and we have to dust ourselves down for the next one.”
At the end of the first half, central defender Richard Wood’s header was disallowed for a foul on goalkeeper Josh Lillis.
Rochdale’s Brad Inman was denied early in the second half by a good stop from Marek Rodak after bursting clear but the visitors deservedly went ahead when Humphrys lashed a shot into the bottom corner following a rapid build-up.
Joe Mattock denied Ian Henderson a second with a well-timed tackle and Semi Ajayi’s late effort for Rotherham was cleared off the line as Rochdale hung on for back-to-back league victories.
Rotherham United: Rodak, Emmanuel (Palmer 77), Ajayi, Wood, Mattock, Forde (Williams 59), Towell, Vaulks, Newell, Smith, Ball (Lavery 69). Unused substitutes: Taylor, Price, Ihiekwe, Yates.
Rochdale: Lillis, McGahey, McNulty, Delaney, Rafferty, Inman (Rathbone 82), Camps, Cannon, Done, Humphrys (Davies 77), Henderson. Unused substitutes: Wiseman, Moore, Adshead, Hart, Alexandru Dobre.
Referee: G Salisbury (Lancashire).