Alex led twice at the New York Stadium but in the end lost 4-2 in a thrilling second half that saw them miss a penalty and the chance to regain the lead.
Bradden Inman gave Crewe the lead after 12 minutes after AJ Leitch-Smith had seen a shoot hit the post.
Chuks Aneke went close to an equaliser with a diving header that flew just wide.
But Rotherham made sure of the win in the dying seconds when Frecklington pounced to shoot home his second as Crewe pushed forward.
Evans said: "It was satisfying after two defeats. We were not at our best for spells but generally I felt we controlled it over the 90 minutes.
"The quality of the goals was special. I was really proud of the players and if we go behind I'm not worried because they always respond in the right way.
"Yes one or two were a notch down but we had players who stepped up and it shows the character we have in this squad. I'm proud to work with them.
"It was a good win for us and the Millers fans were brilliant and they created an atmosphere, so thanks to everyone who turned up and got behind the team.
"I think we were a notch down in the first half but I think people can see we're not idiots. I think its a good win against a good team who had won their last two games."