The result extended Bradford's run of home matches without a win to six, going back three months and means they have lost their last six League and cup matches against Rotherham.
This encounter featured seven bookings in front of a 18,218 crowd - the biggest of the season at Valley Parade.
Evans said: "The game was about character and we had the character. We were dominant.
"There was an electric atmosphere with a big crowd, but I think the Bradford crowd will think they were beaten by a better side on the day.
"The lads were disappointed they didn't win by three or four nil, but I have great respect for Bradford. They have some very good players and they will come back."
After a frantic start, the visitors scored what proved to be the winning goal after 20 minutes through Newcastle loanee, Slovenian Haris Vuckic.
The Bradford defence failed to clear after a surging run from Lee Frecklington and the ball fell to Vuckic, who scored with a superb shot into the far corner from just inside the penalty area.
The home side rarely looked like saving the game in the second half and it needed two fine saves from Jon McLaughlin to prevent James Tavernier from increasing Rotherham's lead.
First, he turned away Tavernier's free-kick from from the the edge of the penalty area in the 48th minute and made a diving save to deny the Rotherham player in the 65th minute after Tavernier made a strong 30-yard run into the penalty area .
The only serious save Rotherham keeper Adam Collin had to make was to keep out a first-half effort from Garry Thompson.
Source PA