Tony Carr's under-19s went down 2-0 at Villa Park in their semi-final clash, while Kevin Keen's younger side could only manage a 1-1 draw in a game they needed to win by two clear goals in order to qualify for the quarter-finals of their respective compeition.
However, both sides can consider themselves unlucky not to have progressed further after impressive performances against Villa that both deserved more than they provided.
The under-19s began their semi-final in determined mood and were by far the better side in a first half that saw them go close to taking the lead on three occasions.
Greg Pearson flashed one shot wide and saw another saved, while Phil Lumsden burst clean through but was also denied by the Villa keeper.
Hammers ended the half firmly in control, but paid dearly for their failure to turn chances into goals, as Villa took the lead early in the second half.
A misplaced pass by Daryl McMahon was seized upon by the opposition and the ball was worked down the left before being crossed for prolific young striker Luke Moore to slot home.
Hammers fought back bravely in an attempt to force an equaliser, and almost did so midway through the second half when McMahon's shot was clawed out by the keeper and dropped to Sam Wright, who seemed certain to score but agonisingly saw his effort cleared off the line.
With 10 minutes remaining, Villa grabbed a vital second. Elliott Ward attempted to shepherd the ball out for a goal-kick, but was dispossessed by an opponent who managed to cross the ball in for the unmarked Hynes to head home and end Hammers' hopes of a place in the final.
Said Tony Carr afterwards: "In the end we are quite disappointed to lose, because our first half performance was excellent and suggested that we would go on and win the game.
"We had three or four good chances and no one would have complained had we gone in one or two up at half-time. We told the lads to make sure they kept the tempo up and pushed on for the all-important first goal, but Villa scored early and it was an uphill task for us after that.
"Their first goal came from a poor pass and the second goal was just sloppy, but that doesn't take away from the very good season that we have had. The players have worked very hard all year and we have got to the last four of this competition, so it is important to recognise what we have achieved.
"It has obviously been a very difficult week for everyone connected with the club, and it's a shame that we haven't finished on a high note, but all the young players here can be proud of their performances today."
Team: Jackson, McClenahan, Tattam, Ferdinand, Ward, Lumsden, Wright, McMahon, Akinsete, Pearson, Cole (Bunce 70). Subs unused: Welsh, Fletcher, Morris, Sealey.
Meanwhile, the under-17s also travelled to the midlands to face Villa and were held to a 1-1 draw that wasn't enough to see them through to the last eight of the competition.
After a 4-1 victory over Middlesbrough and a 2-1 defeat against Everton in their first two play-off matches, Hammers needed to beat group leaders Villa by two clear goals in order to qualify for the quarter-finals.
Their task became even harder when Villa took the lead midway through the first half, but schoolboy defender Jemel Henry drew the Hammers level in the 65th minute when he slotted home a loose ball following a goalmouth scramble.
With nothing to lose, Hammers threw everything forward and went close to taking the lead on a couple of occasions. Liam Parrington and San Lee saw decent efforts saved, while substitute Ollie Allen had a goal disallowed for offside.
Villa took advantage of the spaces left behind by the attacking visitors to create a few chances of their own, but goalkeeper Matt Reed was in fine form to keep his side level.
In the end, a point just wasn't enough, but Kevin Keen had plenty of praise for his young players afterwards.
"We played very well today against a team with a fair bit of quality. They had chances, we had chances and it could have gone either way, so in the end a draw was a fair result.
"It wasn't enough to help us qualify, but the players have done fantastically well to get this far and they have been a joy to work with all season.
"Their attitude and work-rate has been first class and the first year boys are all ready to step up to the under-19s level next season. They have played a lot of football this season, some players have been playing for the under-19s and reserves already, so we have high hopes for all of the young players here."
Team: Reed, Laws, Parrington, Blewitt, Henry, Tucker, Shaw, Cohen, Ephrain (Stokes 75), Collington (White 85), Lee (Allen 70). Subs unused: Behcet, Yao.