Wilder said afterwards, "It was always going to be a difficult game. There have been some victims over the last few years coming here and getting turned over. I thought our attitude was excellent.
"I didn't think it was a great game. We were pragmatic in our approach - we needed to show plenty of things to get the result today."
On his side's chances of an extended Cup run, he added: "If we could get a home draw, with it being a midweek game with all the travel associated, we'd take that. But to go far in this competition there are hurdles you have to overcome.
"Momentum is key. We want to win games of football. Our changes show you what our boys are like. There are some good players not getting game time at the moment. Every game is an opportunity to grasp and some players grasped that opportunity today."