First-half goals from Ben Pringle, Mark Bradley and Daniel Nardiello gave the Millers a deserved win 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 see red in the first half for a deliberate elbow on Alex Revell.
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."
He went on: "We were disappointed with it going to a replay. 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 are 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."
County manager Keith Curle locked himself in the dressing room with the players for almost an hour after the final whistle but said the blame lay at his door.
He said: "First of all I look at myself and I look at my staff. I go back to when we first came in and what we brought to the players and that is what I've been chatting to the players about just now.
"It would be easy to go in there and dismantle a lot of good things that have gone on at this football club and lay the law down, point fingers and tell home truths to make myself feel better.
"I know we need a reaction but results stand at me - I'll take that on board.
"When I came in I said when there are positives and accolades the players take them. I'll take the negatives and that is what I've got to do now. The players have to have the same belief to express themselves and play with a smile on their face."