Spurs needed a minor miracle to retrieve a 3-0 deficit from the first leg in Germany but Pochettino named Harry Kane as a substitute and instead it was Pierre-Emerick Aubameyang's double that secured Dortmund a 5-1 win on aggregate
Son Heung-min added a late consolation for the hosts.
It is the third consecutive year Tottenham have failed to reach the quarter-finals of Europe's second-tier tournament and their hopes of lifting silverware this season now rest entirely on the league, where they host struggling Bournemouth on Sunday.
Pochettino drew criticism after his weakened side were outclassed at the Westfalenstadion but the Argentinean stuck to his guns again here as Dele Alli played only 68 minutes, Kane was left on the bench while Christian Eriksen, Mousa Dembele and Kyle Walker were all omitted from the squad completely.
Dortmund also sit second in the Bundesliga, with a trip to Augsburg to come on Sunday, but the fact their star trio - Aubameyang, Marco Reus and Henrikh Mkhitaryan - all started, even with their commanding lead at kick-off, was proof of the German side's superior commitment to progress.
This was Tottenham's 10th outing in the Europa League this season and Pochettino's men have travelled close to 11,000 miles since their opening fixture in August but in the end they went out with a whimper against the sort of opposition they will face more regularly if they reach the Champions League next year.
The opening quarter of an hour was noteworthy only for a nasty collision between Hugo Lloris and Ben Davies, with the full-back allowed to continue by Tottenham's medical staff for five minutes before eventually being replaced by Danny Rose.
Dortmund had already created five chances at the same stage of the first leg but they only needed one to take the lead in the 24th minute as Aubameyang collected a loose ball 25 yards out and rifled it past Lloris and into the far corner.
It was Aubameyang's 34th goal in 40 games this season and, leaving Spurs needing to score five without reply, effectively put the tie to bed.
The Gabon striker could have added a second when he went clean through moments later but appearing from nowhere was Toby Alderweireld, making an excellent last-ditch tackle before pirouetting his way out of danger much to the delight of the Spurs fans.
Son should have levelled when sent clear by Erik Lamela but Kane's stand-in dragged his finish wide and on the brink of half-time it was left to Alderweireld to perform another emergency rescue, as he rushed back to block Mkhitaryan, who thought he had only Lloris to beat.
As the game drifted past the hour mark, Kane continued to loosen up down the touchline but when the change came it was a energy-saving one as Alli was replaced by Tom Carroll with 21 minutes to play.
The game felt almost irrelevant as it drifted into its latter stages but suddenly there were two goals in three minutes as Aubameyang fired past Lloris from close range before Son intercepted Neven Subotic's under-hit back-pass, rounded the goalkeeper and slotted home.
By the time the final whistle blew the stadium was half-empty but those remaining were still singing at the end, fully aware Tottenham's most important tests are still to come.
Source : PA
Source: PA