The young Magpies conceded twice in the opening ten minutes of their last-eight tie at Moss Lane following quick-fire goals from Kahrel Reddin and Kian Taylor before United's second-string drew level before the half-hour mark courtesy of Garang Kuol's stunning long-range effort and Jay Turner-Cooke's penalty.
Kuol continued his purple patch in front of goal at under-21 level after scoring towards the hour mark, netting a fifth goal in his last seven competitive matches, but despite Joe Nuttall bizarrely failing to convert a penalty for Altrincham in the closing stages, Justin Amaluzor's 90th minute header sent the contest to a penalty shoot-out.
United's youngsters began the shoot-out positively as Magpies goalkeeper James Taylor denied Regan Griffiths but, ultimately, missed conversions from Ellis Stanton, Sean Neave and Leo Shahar resulted in Newcastle's exit from the competition.
In the sixth minute, Newcastle fell behind as Reddin scored for the National League outfit, driving into the box from the left flank before arrowing a low effort into the bottom right-hand corner.
In front of 623 spectators, United's youngsters were dealt a further blow in the tenth minute as Taylor doubled Altrincham's lead, heading home at the front post from Elliot Osborne's teasing corner.
Diarmuid O'Carroll's side responded positively as Kuol netted in stunning fashion as the Australia international picked the ball up from distance before firing an unstoppable long-range drive into the top right-hand corner.
Newcastle equalised in the 29th minute through Turner-Cooke's penalty as the South Shields-born midfielder was brought down inside the penalty area by Altrincham goalkeeper Rob Lainton before cooly stroking a low attempt from 12 yards beyond the Robins debutant.
United's second-string were fortunate on remain level terms shortly after as Lucas Weaver latched onto a dangerous cross from the right byline but could only trickle a low first-time effort wide of the left-hand post before Taylor turned out Nuttall's powerful drive from 25 yards out for a corner before the half-time whistle.
Kuol grabbed his second goal of the night in the 57th minute as the Cairo-born youngster capitalised on a defensive mix-up and, after driving into the box, placed a powerful low effort into the far left-hand corner.
Johnny Emerson went close to doubling the young Magpies' advantage after the hour mark as the Carlisle-born winger, a representative of Scotland at under-19 level, latched onto Kuol's pass but his low first-time effort was palmed out for a corner by substitute goalkeeper Harvey Randle.
Reddin went close to drawing Altrincham level after the winger's close-range shot struck the chest of Magpies substitute Rory Finneran on the goal line before the loose ball kindly fell into the hands of Taylor.
Altrincham were awarded a penalty as Remi Thompson was fouled inside a crowded penalty area but Nuttall failed to convert the spot-kick after appearing to make zero contact with the ball, with referee William Davis awarding a free-kick to the visitors.
Newcastle suffered a crushing blow in the 90th minute as Altrincham equalised through Amaluzor as the Robins substitute rose high inside the box before guiding a header into the top right-hand corner.
In the penalty shoot-out, United got off to a bright start as Taylor denied Griffiths' spot-kick with an outstretched leg before Alfie Harrison slotted his penalty into the bottom right-hand corner.
Reddin converted his spot-kick for the Robins before Stanton's attempt from 12 yards flew over the crossbar but Altrincham were unable to take advantage as Jake Cooper also fired a wild effort over the bar.
Turner-Cooke successfully converted from 12 yards for a second time of the night but after Matty Kosylo and Amaluzor scored from the spot for the hosts, either side of Sean Neave's saved penalty for the visitors, Shahar fired his penalty over the crossbar, resulting in Altrincham's passage into the semi-finals.
Newcastle United Under-21s: James Taylor, Leo Shahar, Cathal Heffernan (c), Ciaran Thompson, Dylan Charlton, Scott Bailey (Rory Finneran 46), Ellis Stanton, Garang Kuol (Matheos Ferreira 90), Johnny Emerson (Alfie Harrison 75), Jay Turner-Cooke, Sean Neave.
Subs not used: Luke Craggs, Will Anderson, Joe Brayson, Darren Palmer.
