The Reds hit League Two Burton Albion for five goals without reply as Wilson saw his side into Round Two.
"Cup football is about being in the hat for the next round and, by hook or by crook, you want to get through," said Wilson.
"If you can put a good performance in and get some goals then it's a bonus - and today's a big bonus for us.
"I thought we started the game great. The tempo and the way we took the game to them showed our intentions. We had good opportunities in that period and didn't quite take them.
"They wrestled themselves back into the game somewhat which was credit to them. We knew the first goal would be important and we've got it.
"Second half - we were excellent at times. Some of the football was sublime.
"To run in five goals in a tight game is pleasing."
Conor Hourihane and Devante Cole scored a goal each but Sam Winnall grabbed the headlines as he bagged himself a hat-trick.
Speaking of Winnall, Wilson said, "He's an opportunist. In and around the box, he's in the right spot.
"He's unfortunate with his first effort at goal for the hat-trick. But he's deserved his luck because he's worked hard for it."
