Michael Smith scored a goal in each half against the lowly Railwaymen, who had Scott Robertson sent off in the second half.
There was a lengthy delay when a linesman was hit by a coin which appeared to have been thrown from the away fans section at Gresty Road.
There was a second break in the game as the linesman was replaced by the fourth official after complaining of “dizziness”.
“It’s embarrassing and it is completely unacceptable. If it was one of our fans and it has been seen by CCTV then the culprit should be punished,” said Warne.
“I apologised to the four officials and our captain [Richard Wood] went over as well to see that he was all right too.
“It’s a concern for me as a human being. If that was one of my fans that is found to have done that then they should be punished.”
Rotherham are now investigating the incident as Warne’s side moved back to the top of the table, one point above Wigan.
Warne added: “It was a massive three points as this is not an easy place to come.
“Crewe came at us with the wind behind them in the second half but we managed the game really well. The sending off had a big part to play as we scored from the free-kick.”
Crewe Alexandra: Richards; O’Riordan, Sass-Davies, Offord; Mandron, Lowery, Murphy, Finney (Ainley 75), Johnson (Robertson 38); Long, Porter (Sambou 75). Unused subs: Jaaskelainen, Griffiths, Lundstram, Salisbury.
Rotherham United: Vickers; Edmonds-Green (Harding 79), Wood, Harding; Ogbene, Wiles, Barlaser (Lindsay 87), Rathbone, Ferguson; Smith, Grigg (Kayode 65). Unused subs: Johansson, Odoffin, Miller, Ladapo.
Referee: B Speedie (Merseyside).