Alan Sheehan opened the scoring from the penalty spot after Andrew Shinnie had been tripped, before Kazenga LuaLua got his first for the Hatters with a well taken finish.
Jorge Grant grabbed the Town's third as he nodded in after Aaron Jarvis' effort was saved.
With Peterborough losing on penalties to Brighton & Hove Albion Under-21s, Town have finished top of the group and will play at home in the next phase of the competition.
Jones said: "I am delighted, apart from a nine minute period in the second half I thought we were dominant in everything we did.
"I thought we were excellent, we probed. We got the penalty and the first goal and then Kaz who was just magnificent all night got the second. Then second half we should have won by five or six goals. I am not being disrespectful, we've had clear cut chances where they have tried to come out and we have hit them on the counter as has happened in every home game we've played so far.
"I am very pleased because we have been stretched a little bit with our squad. JJ, Shinnie, Grant and Rea have had to double up with games – we don't like doing that.
"But we've had so many injuries that we've had to do it, but I thought we were magnificent and that's why I love my football club because they're right at it the boys to be fair and they were class tonight, a touch of class."