First-half goals from Ben Pringle, Mark Bradley and Daniel Nardiello gave the Millers a deserved win on Tuesday and set up a third-round tie at Aldershot.
It was a miserable night for County, whose poor home form continued and they saw defender Damion Stewart sent-off in the first half for a deliberate elbow.
Evans said: "I couldn't win a game in the FA Cup until a few years ago, but I do think when you get success in it, and I'm not talking about the financial rewards, I'm talking about when you see your players playing against the top teams there is nothing quite like it."
Evans said he was proud of his team's performance after they dominated a sluggish County from start to finish.
He said: "We were disappointed with it going to a replay and it was 3-0, but it could have been six or seven, but we would have taken a scrappy 1-0 win.
"When we play like that we're difficult to deal with and we played even better than that against Gillingham and lost - football is a strange game.
"To come to Notts County, who are a good side with a good manager and to win in the manner in which we did, which was as comfortable an away performance as you will see in the cup, is testament to the players, who I thought were excellent."