United clinched their first major trophy for six years as Casemiro's header and an own goal from Sven Botman sealed their mature 2-0 win at Wembley.
Ten Hag's first season as United manager has proved transformative for a club in turmoil when he arrived from Ajax last year.
The Dutch coach has steered United to third place in the Premier League, and they remain in contention to add the FA Cup and Europa League to the first trophy of his reign.
United's composed performance against a Newcastle team desperate to win their club's first trophy for 54 years showed the impact Ten Hag has made.
But the demanding Ten Hag has no intention of letting his players rest on their laurels.
"Silverware shows something, that you are on a good pathway. It is one cup and it is February but it shows we are in the right direction," Ten Hag said.
"We have to continue on this pathway and not be satisfied, because satisfaction leads to laziness and then you don't win any trophies."
United haven't won the Premier League since Alex Ferguson's final season in 2013 and they have watched bitter rivals Manchester City establish themselves as England's preeminent force in the meantime.
Winning the League Cup would have been a minor feat in the Ferguson era, but Ten Hag insisted it was essential to his Old Trafford revolution as it provides tangible proof to his players that they can thrive if they follow his methods.
"This moment you have to celebrate. It is not a common day. We won a trophy. This trophy means something. That is the feeling I get," Ten Hag said.
"It will help, it will bring even more confidence as long as we don't go over the top.
"We can give even more, to be better and to be more of a collective. Don't be satisfied."
Ten Hag and his players were joined in the post-match dressing room celebrations by United co-owner Avram Glazer.
The American was attending his first game since the November announcement that his family were considering selling the club.
The Glazers have received offers from British billionaire Jim Ratcliffe and a consortium led by Qatari banker Sheikh Jassim Bin Hamad Al Thani.
United's long-awaited silverware and the rapid improvement under Ten Hag might make the Glazers reconsider ending their unpopular reign at the start of what could be a golden era.
Asked about Glazer's interactions with him, Ten Hag said: "He was really happy. He wants to be part of it as an owner, you feel that.
"The way he is here shows he is committed. But about the process that is not for me. Others in the club are involved in decisions about the ownership."
