Jones said: "I couldn't be happier with where we are today. The boys have been magnificent – every single one of them.
"These characters are outstanding and you feel for them at times when they're giving everything they've got. The reward for the lads is a great feeling."
The visitors made a flying start with two goals in the opening five minutes.
Butterfield was the first to strike with a well-struck effort from the edge of the area in the second minute.
Radlinger then did well to prevent Collins from scoring his second goal of the match, turning the ball wide.
Cornick added a third goal in the 31st minute when a free-kick was headed down and he hammered the ball into the net.
Wilks reduced the arrears with 18 minutes left, firing in after Alex Mowatt played the ball across the box.
Jones added: "I think we need to enjoy the win and the performance because we were ruthless at times and I mean ruthless. If we'd have been five-nil up at half-time, nobody could have complained.
"We had to show a dogged side and defend as a group. I was really, really pleased. I think we played a different way to the way we played in the opening four games of the season.
"I felt we could hurt them and we just changed the game a little bit. I like the fact we've got different styles in our system because we're going to need that.
"I knew we were really close but there comes a time when you have to win a game of football, no matter who you are.
"The psychological barrier was getting broken down week by week. I think we'll take a lot psychologically from it."
Barnsley head coach Daniel Stendel said: "It was a big chance for us to take the second three points but our start was so bad with two goals after five minutes for Luton.
"We were insecure and it was hard. We were prepared for the game and the atmosphere yesterday was good but the start wasn't.
"You cannot play like this in the Championship and this was the big experience from the game.
"We need to apologise for the first half. The supporters can have expected more from us.
"We need to come back to our best performances. The most things you can learn in the worst situation.
"This is our team and our situation at the moment and next week is another game.
"We missed experience but this is our squad. We have no experience and no player with 200 games in the Championship and this is the situation at the minute.
"I learn things and we need to improve. I think we will do it."