The Hatters took the lead through Luke Gambin 20 minutes in before the visitors responded immediately as Joe Pritchard's shot hit the post but bounced in off keeper James Shea. Spurs went ahead just two minutes after the restart as Ryan Loft slotted home, but the score was levelled when Josh McQuoid headed in from Jack James' back stick cross.
With the scores level, Checkatrade rules dictated the game went to penalties, with Luke Gambin scoring the final one in a 4-2 victory for Jones' side.
The Hatters manager said: "I thought it was an excellent game. Tottenham are a good under-21 side, they came out and they play and they are a very sharp and they gave us a real good test out of possession.
"We started very well, we should have been a couple up, we had a couple of great chances. We finally took the lead and then sloppiness gave them an equaliser. But I thought it was a thoroughly entertaining game.
"[It was] a bit end-to-end for how a manager would like, I thought we had enough chances to have won the game, but we are very pleased. It was a very good run out.
"We were very, very attack minded. We started with two front men, we had a front man at number ten, we had a front man at the side of the diamond, we had Luke Gambin there as well. Effectively we had a real front five.
"I thought they worked really hard and as I said it was a good run out. It was a real good test for some of the younger ones as well. Which was very pleasing."