Playing in torrential weather conditions, the Toon teenagers fell behind before the half-hour mark at Whitley Park following David Angibeaud's close-range finish.
The hosts, however, conceded three times in the second half as Benjamin Casey's clinical effort doubled Palace's lead before quick-fire strikes from Angibeaud and Casey rounded off a tough evening for United's youngsters.
Four changes were made from Saturday's Under-18 Premier League North defeat against Liverpool as Mason Miley, brother of Lewis, was named in the starting XI as well as Matheos Ferreira, Rory Finneran and Noah Morgan.
With a fifth round tie away at Stevenage awaiting the winner, Ferreira created the opening chance in front of goal. The Ashington-born winger, who netted a hat-trick in Newcastle's 5-2 win against Portsmouth in round three, drove a swerving effort at goal but the ball was held by Palace goalkeeper Jack Mason.
The young Magpies trailed in the 29th minute as Angibeaud netted for the visitors. As Jasper Judd's in-swinging corner landed inside the six-yard area, the Newcastle defence were unable to clear to safety, with Angibeaud stabbing the loose ball home from close-range.
Roman Dowell, a representative of England at under-17 level, prevented Palace from doubling their lead as the Hebburn-born goalkeeper stood tall to block Benjamin Casey's strike after the ball initially broke kindly into the striker's path inside the box.
Newcastle were unfortunate not to level on the stroke of half-time as Matty Taylor raced onto Miley's through pass but the 17-year-old midfielder elected to pass instead of, arguably, firing at goal. The ball was blocked inside the box before Taylor's rebound pass was turned out of the penalty area.
After an even opening to the second half, Mills was unable to equalise for the young Magpies as the 16-year-old winger, who joined the club from Port Vale in 2023, raced onto a dangerous forward pass but his tame effort was comfortably held by Mason.
Newcastle were dealt a tough blow in the 66th minute as Casey netted Palace's second goal of the night. After Dean Benamar intercepted Finneran's pass, the ball eventually worked its way to Casey before the Palace forward rifled the ball into the roof of the net.
Mills went narrowly close to halving the deficit after latching onto Henry Johnson's headed knockdown inside the box but his first-time effort was turned around for a corner following Mason's impressive one-handed stop.
In the 75th minute, Newcastle conceded a third goal as Agnibeaud grabbed his brace, connecting with Benamar's low cross from the left flank before firing home inside the six-yard area.
Newcastle's difficult night continued as Casey netted his second goal of the tie, collecting Stuart Oduro's pass before placing a low attempt from the edge of the box into the bottom left-hand corner.
Newcastle United Under-18s: Roman Dowell, Noah Morgan, Jake Durrant, Isaac Moran, Henry Johnson (c), Rory Finneran, Matheos Ferreira (Jack Patterson 88), Mason Miley, Kacey Wooster, Matthew Taylor (Sammy Pinnington 70), Michael Mills (Alfie Hutchison 80).
Subs not used: George Mair, Ezra Tika-Lemba, Kayden Lucas, Ethan Ndiweni.
