A bizarre first half winner from Villa's Connor Taylor proved the difference over the two legs and Newcastle were unable to pull themselves level.
The Magpies enjoyed plenty of possession but, particularly when striker Philip Airey was sent off for his second caution 14 minutes from time, they rarely tested goalkeeper Benjamin Siegrist.
In the end Joe Joyce, the academy director of the Tyneside, still harbours hopes of producing a crop that emulates Paul Gascoigne, Paul Stephenson, Joe Allon et al in 1985.
First team boss Chris Hughton, whose side could be confirmed as Championship champions later today without kicking a ball, was among the near 5,000-strong crowd to witness the defeat, along with owner Mike Ashley and Derek Llambias.
But Newcastle, who have regularly reached the latter stages of the competition over the last decade, once again found that reaching the final was a step too far and it is Villa who face Chelsea.
After an early scare when Taylor's delivery from the left evaded a crowded penalty area, there was an increase in confidence that this could be Newcastle's season.
Despite plenty of possession in the opening half, opportunities were few and far between. The best two for Newcastle both fell to lone-striker Airey, but neither ended in the opener.
Airey, the scorer of the first goal of the two legs last week, headed over from left-back Paul Dummett just before the quarter of an hour mark. He was also denied when his shot, unmarked at the back post, was blocked by defender Danny Devine.
Plenty of neat passing, however, was not enough to separate the teams and then Joyce's men had it all to do when Villa opened the scoring 11 minutes before half-time.
There was more than an element of fortune about it. When Taylor headed goalwards from Samir Carruthers' centre, goalkeeper Jak Alnwick's dived to his right but the push only turned the ball on to the post and over the line.
An injury, which looked serious after a challenge from Carruthers, brought an end to Newcastle captain Jeff Henderson's semi-final, but his departure led to a double change that brought fresh impetus to the home team.
Haris Vuckic, brought on along with full-back Patrick Nzuzi, was quick to make an impression. The Slovenian, being monitored regularly by Chelsea, struck low from distance and goalkeeper Benjamin Siegrist failed to gather.
Newcastle, however, failed to make the most of the loose ball and that became the story of the second half, with Villa regularly counter-attacking in the hope of adding a second.
And on the hour the Newcastle crowd must have feared it was not going to be their night when Samuel Ameobi's near post header from Samuel Adjei's corner was cleared before the latter's left foot curler shaved the top of the bar.
But when Airey was shown his second yellow card, which could have been a straight red for stamping on Carruthers, the chances of a comeback receded and Carruthers went close to adding a late second when he hit the post.
Goals: Taylor (34, 0-1) Bookings: Dummett (43, foul); Airey (45, foul) Sent off: Airey (76, second bookable offence) Referee: Gary Sutton (Lincoln) 6 Attendance: 4, 959 Entertainment: *** NEWCASTLE UNITED (4-5-1): Alnwick 6; Tavernier 7, Henderson 7 (Nzuzi 46, 6), Folan 7 (McGorrigan 90), DUMMETT 8; Ameobi 6, McDermott 6 (Vuckic 46, 7), Inman 6, Newton 6, Adjei 6; Airey 6. Subs (not used): Robinson, Taylor.
ASTON VILLA (4-4-2): Siegrist 7; Berry 7, Williams 7, Devine 7, Deeney 7; Simmonds 6, Blythe 6, CARRUTHERS 8, Roberts 6 (Nelson-Addy 31, 6); Taylor 6, Poyser 6 (Cameron 90). Subs (not used): Barrett, Dyer, Johnson.
MAN OF THE MATCH: Samir Carruthers Newcastle fans might not like it, but he was a menace from start to finish.