The young Magpies, requiring a win to keep their hopes of qualifying for the quarter-finals alive, trailed inside the opening two minutes of their penultimate Group C clash at Whitley Park following Kaloyan Bozhkov's slotted finish.
Sven Sunta's clinical effort doubled the visitors' lead shortly after the restart before Patrik Horvat's dinked effort rounded off a tough afternoon for United's second-string, who conclude their participation in this season's competition with a home clash against Benfica next month.
Newcastle got off to a difficult start as Zagreb scored within the opening 75 seconds as Cathal Heffernan's pass was intercepted by Patrik Horvat before the ball kindly worked its way into Bozhkov's path, who slotted a low first-time effort from the edge of the box beyond Magpies goalkeeper James Taylor.
The hosts went close to levelling the scoreline shortly after as Seung-soo Park, who joined the Magpies from Suwon Bluewings last summer, cleverly evaded his marker before picking out Joe Brayson inside the penalty area but the 18-year-old striker, son of former Newcastle forward Paul, saw a side-footed attempt blocked by the right foot of Zagreb goalkeeper Tai Znuderl.
Taylor produced a key stop to prevent Zagreb from extending their advantage as Park's pass was intercepted by Horvat, who advanced towards goal before his attempt at goal was parried by the Kettering-born teenager, with defender Charlie McArthur heading the ball away from danger.
The young shot-stopper was forced into action before the half-time whistle as Zagreb defender Noa Mikic won possession towards the right flank before his fierce strike from the edge of the box was beaten away by Taylor before McArthur hooked the loose ball clear for a corner.
Newcastle were delivered a tough blow in the 50th minute as Sunta netted Zagreb's second goal of the game, latching onto the ball inside the penalty area before placing a powerful first-time effort beyond Taylor.
United's youngsters conceded a third before the hour mark as Horvat scored for the Croatian outfit. After Taylor's intended clearance was intercepted by Mislav Cutuk, the Zagreb midfielder slipped the ball into Horvat's path, who beat the Newcastle goalkeeper to the ball before lifting his attempt into an empty net.
The hosts almost pulled a goal back in the closing stages as 17-year-old winger Matheos Ferreira, who netted a hat-trick in Tuesday's FA Youth Cup third round win against Portsmouth, raced onto Mason Miley's impressive pass but despite lifting the ball over Znuderl, Zagreb skipper Marko Zebic was alert to hack the ball off the goal line.
Newcastle continued their push for a goal as Park blocked Znuderl's intended pass towards the right flank before the South Korea Under-20 international, who made his full Magpies debut for Eddie Howe's side in a 2-2 draw against RCD Espanyol at St. James' Park last summer, eventually saw his stabbed effort from a tight angle blocked by the Zagreb shot-stopper.
United's second-string had the ball in the net during stoppage-time as Park's fierce drive from the edge of the box was pushed into McArthur's path by Znuderl, with the Kilmarnock-born defender firing the rebound in the net, but the goal was disallowed as the Scottish centre-back had strayed into an offside position.
Newcastle United Under-21s return to competitive action in the New Year when hosting their Middlesbrough counterparts at Whitley Park in the Premier League 2 on Friday, 9th January (kick-off 7pm GMT).
Newcastle United Under-21s: James Taylor, Ciaran Thompson (Logan Watts 90), Dylan Charlton, Charlie McArthur, Cathal Heffernan (c), Rory Finneran, Kyle Fitzgerald (Matheos Ferreira 61), Sam Alabi (Baran Yildiz 80), Joe Brayson (Ben Parkinson 45), Darren Palmer (Mason Miley 61), Seung-soo Park.
Subs not used: Adam Harrison, Henry Johnson.
Photohgraph courtesy of Finlay Henderson.
