After recording the biggest comeback in the competition's history in the previous round against Paris Saint-Germain, Barca were unable to repeat the feat against Juve, who backed up their stunning first-leg win with an obdurate rear-guard display.
Lionel Messi missed the home side's best opportunities, firing off-target from close range in either half, the story of a match that saw his side rack up 19 shots but only test Gianluigi Buffon with one of them.
Juve – beaten by Barca in the 2015 final – have now reached the semi-finals in two of the last three years as they look to win a first European crown since 1996.
In stark contrast to the previous round, Neymar was reduced tears at full-time as Barca went out in the quarter-finals for the third time in four seasons to leave the outgoing Luis Enrique's hopes of winning a major trophy in his final season dependant on LaLiga and the Copa del Rey.
But a trip to Santiago Bernabeu for a pivotal match against El Clasico rivals and league leaders Real Madrid coming up on Sunday gives Barca little time to lick their wounds.
Juve - unchanged from the first leg - threatened twice early on as they searched for an away goal, Gonzalo Higuain firing over from a decent opening, while Juan Cuadrado hooked an acrobatic attempt off-target.
Luis Enrique reverted to Barca's tried-and-tested 4-3-3 system, with Sergio Busquets and Jordi Alba coming into the side, and the left-back had the hosts' first opportunity of note when, on the stretch, he diverted Messi's precise pass wide.
A better chance went begging a few moments later when Messi lashed a left-footed strike wide from 15 yards after Luis Suarez's flick had set him up.
Barca continued to probe as Neymar's volleyed effort flew just past the post, before Buffon was the first goalkeeper to be tested, the veteran diving to keep out Messi's deflected strike from the edge of the area.
Juve created a good chance of their own before half time, but Higuain could only shoot straight at Marc-Andre ter Stegen, having been picked out by Miralem Pjanic as a fiery contest – which saw Andres Iniesta and Neymar booked – reached the interval without a breakthrough.
The visitors came so close early in the second half, Cuadrado narrowly missing the target after an incisive breakaway, before Ter Stegen denied the winger with another effort moments later and had to keep out a Pjanic shot which took a wicked deflection.
Barca, meanwhile, saw Neymar and Messi come close without testing Buffon, prompting Luis Enrique to bring on Paco Alcacer for Ivan Rakitic in an attacking change.
It was Messi who missed Barca's best chance midway through the second half, volleying over with his right foot from eight yards after Buffon had flapped at a corner, allowing Suarez to find the Argentina international with the goal gaping.
Sergi Roberto, the hero of the last round, shot wide as time began to work against Barca, while Paulo Dybala did the same at the other end prior to being replaced by defender Andrea Barzagli in a sign Allegri was ready to fully shut up shop.
Luis Enrique even threw Gerard Pique into attack for the final stages but Barca were out of ideas and Juve joyously celebrated a famous victory when the full-time whistle arrived.
KEY OPTA STATS
- Barcelona failed to score in both legs of a Champions League knockout game for the first time since the 2012/13 semi-final against Bayern Munich.
- This match ended Luis Enrique's 100 per cent home Champions League record at the Nou Camp – he had won all 15 previous matches before tonight.
- Barcelona have now failed to reach a Champions League semi-final in back to back seasons for the first time since 2004/05, when they went three in a row without one.
- Lionel Messi had five shots off target in the match, his most in a Champions League game since September 2015 against Roma (also five). Only once before has he attempted more off target in a Champions League match (six vs BATE Borisov in 2011).
- Gianluigi Buffon has now kept 46 clean sheets in the Champions League - only Iker Casillas (54), Edwin van der Sar (50) and Petr Cech (47) have more than the Italian.
- Of teams to have attempted 15 or more shots in a Champions League match this season, Barcelona tonight had the lowest percentage of those shots on target (5% - 1 out of 19).
- Juventus haven't conceded a single goal from open play in this season's Champions League, going a full 900 minutes without conceding.