Jorge Grant and Elliot Lee got the goals for the Hatters in a much changed side from the one that was defeated by Norwich City on Wednesday evening.
Jones said: "Notts County are a very good League Two side, so we knew it would be the equivalent of playing a League One side basically.
"They've strengthened well so we knew it would be a realistic test for us. I am delighted, from start-to-finish I thought we were excellent, I thought we controlled the game. We lacked a little bit of sharpness if I am going to be ultra-critical, especially in the final third. Overall I am delighted and it's always good to win.
"I thought we moved the ball around well for a sticky pitch, on a hot day we moved the ball very well. I am pleased, as I said it was just a lack of sharpness in the final third. Cornick has had a couple of chances. We've had a few where the interchange just isn't quite there, but as we go down the weeks, that will sharpen up.
"[Jorge Grant's goal] was a bit of an instinct shot, we cant give him that. the build up play we work on, but that is a little bit of instinct, it's a great shot and it's given the keeper no chance, to hit them in on off the post is very difficult to save those and that's why we brought Jorge here.
"We like to play fluidly, we like to score goals and Jorge has got big boots to fill in terms of I think Olly got seven, we're looking for a bigger return from Jorge."