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 their star trio - Aubameyang, Marco Reus and Henrikh Mkhitaryan - all started.
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 Toby Alderweireld, made an excellent tackle.
Son should have levelled when sent clear by Erik Lamela but Kane’s stand-in dragged his finish wide and on half-time it was left to Alderweireld to perform another emergency rescue to block Mkhitaryan.
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 sparked to life again and Aubameyang fired past Lloris from close range before Son intercepted Neven Subotic’s under-hit back-pass, rounded the goalkeeper and slotted home.
Lloris, Trippier, Alderweireld, Wimmer, Davies (Rose 13), Dier, Mason, Lamela (Onomah 74), Alli (Carroll 69), Son ,Chadli.
Weidenfeller ,Piszczek, Subotic, Papastathopoulos (Durm 54), Schmelzer, Ginter,Castro,Weigl, Mkhitaryan (Kagawa 71),Aubameyang,Reus (Pulisic 60). Referee: N Rizzoli (Italy).