Jordan Rhodes' goal eight minutes from time was all that separated the sides as more than 2,300 travelling Hatters sang their hearts out, but had to make the long journey home to Bedforshire with pride in a brilliant season, but no Wembley final at the end of it.
Manager Nathan Jones made two changes to the side that started the first leg at Kenilworth Road on Friday night.
Robert Snodgrass came in from the off in place of the injured Henri Lansbury, whilst Danny Hylton started up-front alongside Harry Cornick.
Cameron Jerome was named amongst the substitutes alongside top scorer Elijah Adebayo, who returned to the squad after missing the last three games through injury.
After a couple of early corners, the Hatters had the first sight of goal in the seventh minute when the high press earned reward with Snodgrass winning possession 35 yards out to slip Cornick into the box, but the striker's
Cornick had an even better chance to add to his 13 goal tally four minutes later when Allan Campbell released Kal Naismith on the left. The centre-half's low cross was straight into the former Bournemouth man's path, only for his shot to be kept out by goalkeeper Lee Nicholls' chest.
Snodgrass was next to have a go, James Bree and Cornick combining on the right to tee the ex-Leeds midfielder up for a 20-yard curler that Nicholls punched away, with Amari'i Bell unable to divert his follow-up effort on target.
Huddersfield registered their first effort on goal in the 19th minute, Danny Ward meeting Danel Sinani's cross from the left with a header that flew safely over Matt Ingram's crossbar.
The Hatters were playing with confidence and urgency, suffocating the Terriers into conceding possession inside their own half, and the next oopening came from Bree's angled cross-shot on the half-hour mark, Nicholls again pushing the ball out and needing to be helped behind by a defender.
Huddersfield cleared the first corner behind, but Bree's second delivery from the left was flicked on by Hylton at the near post and somehow mananged to elude both Campbell and Jordan Clark in the six-yard box to run behind for a goal-kick.
Clark fired straight at Nicholls in the 36th minute after he had once again won the ball in the hosts' third, Snodgrass, Cornick and Bell linking up to return the ball to the midfielder to shoot from the edge of the box.
Huddersfield had their first shot on target a minute later when Harry Toffolo waltzed into the Town box, only to find Ingram flying to his left to deny the in-form left-back with a fine save.
The hosts' top scorer Ward was forced off by injury on 41 minutes, to be replaced by veteran forward Rhodes, but it was Town who were once again the more progressive in an attacking sense, Bree testing Nicholls from 25 yards two minutes from the end of a first half in which they had done everything but score.
Huddersfield came flying out of the traps after the break, winning a corner that caused concern in the Hatters' six-yard box, before Sinani delivered a second ball to the far post where Tom Lees headed over the bar.
Sinani had a crack himself on 49 minutes, Ingram saving comfortably down by his near post, and the Hatters were soon on the attack again, Campbell crossing from the right for Bell to head narrowly wide at the other end.
Clark became the first into ref Peter Bankes' notepad just before the hour for a sliding challenge on Rhodes, before Naismith followed suit moments later for a foul on Sorba Thomas, soon after the Terriers sub had been introduced.
Huddersfield had the ball in the net on 65 minutes when Lees met Thomas' free-kick with a firm header, but ref Bankes had already blown for an infringement on the edge of the box.
Jerome, on in place of Hylton, headed a Snodgrass free-kick a foot wide with 20 minutes to go. The veteran forward then slipped Cornick in on the right side of the area for another angled drive that Nicholls parried into Bree's direction, but the ball wouldn't come down for the right-back to fire at goal.
Huddersfield drove forward at the other end, with Ingram making a fine double save before surviving a penalty shout for a tangle with Toffolo as the Terriers defender tried to pounce on the loose ball.
The Yorkshire side finally broke the deadlock with eight minutes to go when Thomas delivered another curling free-kick into the box and Rhodes steered the ball in at the far post.
It was enough to book the Terriers' place at Wembley, with the Hatters left to reflect on a night of missed opportunities, but a campaign in which every single member of the squad, staff and club as whole has done Luton Town proud.
COYH!