The Toon teenagers, targeting back-to-back league wins after a 3-2 away victory against Liverpool last month, trailed inside six minutes at Finch Farm following Justin Clarke's finish before Braiden Graham's penalty doubled the Toffees' lead.
Clarke extended Everton's advantage ten minutes after the restart before Sean Neave, a representative of England at under-17 level, cut the deficit for the young Magpies with a fourth goal in his last three league games at under-18 level.
Joe Brayson, son of former Magpies forward Paul, pulled a goal back for the visitors in the final minutes of the league clash but Chris Moore's side were unable to grab a stoppage-time equaliser in the five-goal encounter.
Newcastle United Under-18s: Will Anderson, Henry Johnson (Sam Alabi 58), Logan Watts, Luke Craggs (c), Guy Bloomer (Noah Morgan 18), Alex O'Donovan (Luke Gilligan 79), Mason Miley (Ezra Tika-Lemba 58), Kacey Wooster, Matheos Ferreira, Sean Neave, Joe Brayson.
Subs not used: Tyler Jones.