Neil Winskill's side got off to a nightmare start after conceding twice in the opening eight minutes at St. James' Park following Paul Appiah's header inside 67 seconds and Brad Young's clinical finish.
After Carney Chukwuemeka netted Villa's third before the half-hour mark, left-back Josh Scott's tidy finish on the stroke of half-time restored hope for the young Magpies.
However, Chukwuemeka completed his hat-trick with two goals in two second-half minutes before substitute Kahrel Reddin netted the Villans' sixth to complete a disappointing end to the Toon teenagers' cup run.
Newcastle had beaten Huddersfield Town, Leeds United and Watford to reach the last-eight of the prestigious competition but faced a Villa side who had netted 16 goals in the tournament, thrashing Burton Albion 9-0 in round five.
A home tie against West Bromwich Albion awaited the winners of the last-eight clash, with Newcastle bidding to reach the semi-finals of the tournament for the first time since 2010.
In the 2nd minute, though, Newcastle fell behind as Appiah rose high from Hayden Lindley's corner and nodded the ball into the far right-hand corner to break the deadlock.
Six minutes later, Villa doubled their lead as Young latched onto Arjan Raikhy's inviting pass before tucking the ball beyond United goalkeeper Max Thompson.
Elliot Anderson, who made his senior debut for the Magpies in January's Emirates FA Cup defeat at Arsenal, went close to halving the deficit after cleverly nutmegging Appiah on the left wing before the under-18 skipper saw his low deflected strike crash off the side-netting.
The visitors grabbed their third of the night in the 28th minute through Chukwuemeka as the 17-year-old midfielder collected a short corner before jinking into the area and firing a curling strike into the right-hand corner.
In the 45th minute, United were handed a lifeline in the tie as Scott pulled a goal back for Newcastle.
The Gateshead-born left-back controlled Anderson's pass, after the England under-19 international had managed to evade the challenge of a pair of Villa defenders, before squeezing his low effort into the far right-hand corner.
In the second-half, United's youngsters made a promising start as Lucas De Bolle, who scored and registered an assist in United's fifth round victory against Watford, saw a low strike blocked by the legs of Villa goalkeeper Filip Marschall.
However, Villa regained their three-goal cushion in the 62nd minute as Chukwuemeka grabbed his brace. After Raikhy capitalised on a loose ball in a dangerous area, the central midfielder's early pass found Chukwuemeka who emphatically placed the ball into the bottom right-hand corner.
In the 64th minute, United's youngsters were punished further as Chukwuemeka completed his hat-trick after Louie Barry's pass found the England under-17 international inside the penalty area, who calmly converted past Thompson.
Villa grabbed a sixth goal in the 76th minute as Reddin, introduced at half-time, feigned to shoot before cutting inside to bury his effort into the far left-hand corner.
Newcastle United Under-18s: Max Thompson, Joe Oliver, Harry Barclay, Josh Nicholson, Josh Scott, Nathan Carlyon, Reagan Thomson (Kyle Crossley 60), Jamie Miley, Lucas De Bolle (Josh Gilchrist 88), Elliot Anderson (c), Dylan Stephenson (James Huntley 72).
Subs not used: Josh Stewart, Oliver Marshall, Lewis Brannen, Michael Ndiweni.
