The game was settled by the hosts' skipper Johnny Mullins in the 57th minute as he rose above a crowded goalmouth to head home David Noble's right-wing corner
"When we play like that, we are very, very hard to contain," said Evans after his first local derby at New York Stadium.
"As a manager, if every local derby is as one sided as that, I'll be happy.
"We produced a really good performance and that's against a Chesterfield team I have the highest regard for, but when our team play like that we are very, very hard to contain.
"We've won a game against difficult opposition in a local derby but I've just reminded the players we've done nothing and you only get the same for beating Chesterfield as you do for beating the other teams.
"That win was for our supporters because they have had a couple of disappointments recently, but they can go away and talk highly about the quality of that performance.
"If people see a better passing footballing side than that in League Two they should send it to me on a postcard quick because I've never seen one.
"But people rarely give Rotherham United the credit they deserve, but they deserve credit for that performance. We have given our supporters some fantastic performances this season.
"The consistency factor comes into it but if I can get my team to perform with the passion they have shown, we'll take the results as they come."