The Hammers lost 2-1 on the night and 4-3 on aggregate despite at one stage leading 2-0 and then 3-2 over the course of the two legs.
The crucial period of the tie, and where it all went wrong for Slaven Bilic's side, was in the last half an hour of the first leg at Upton Park as the visitors scored two precious away goals following James Collins' sending off.
It was undoubtedly West Ham's toughest test in the competition so far and proved valuable experience for a number of young and inexperienced players that were given their chance, particularly in the second leg.
But what did we learn from the match?
1) Manuel Lanzini could be a useful player for West Ham's first team
West Ham's best player in the first half on his competitive debut, which he marked with a lovely goal. But the 22-year-old Argentine's lack of fitness caught up with him in the second half as he faded badly and was virtually anonymous apart from a few wasted scooped passes to try and pull off the spectacular. Plucked from the obscurity of the UAE League where he had made a somewhat bizarre switch to join Al Jazira, Lanzini has shown enough against Werder Bremen and FC Astra Giurgiu to suggest that he has the ability to shine for the Hammers and could prove a very useful player if he can maintain his level of performance over 90 minutes. May well raise his game if playing in West Ham's first team with better players.
2) The future is bright but youngsters must now get out on loan
One thing West Ham's Europa League journey has shown everyone is how many talented young players the east Londoners have emerging from their famed Academy. After a very barren spell over the past few years, Slaven Bilic has the likes of Reece Burke, Reece Oxford, Lewis Page, Kyle Knoyle, Josh Cullen and Elliot Lee all coming through. All of those players have featured in Europe for the Hammers this summer but now the club have been dumped out, their futures will more than likely be on loan if they are to progress and become the players they threaten to be. All have performed admirably this pre-season, particularly Oxford, who at 16 has become the club's youngest ever player. But in Romania, Page and Knoyle both showed great potential, with Page in particular earning praise from the likes of BT Sport pundit and former England manager Glenn Hoddle.
3) Slaven Bilic was damned if he did and damned if he didn't
Having been banned from the touchline and changing rooms against FC Astra after being sent to the stands in the first leg at Upton Park, Bilic went to Romania with one hand tied behind his back. Forced to watch on helplessly from the terraces again, the former Croatia boss elected to send out a youthful shadow side to save his first team for Sunday's Premier League opener against Arsenal. The Hammers are now out of Europe and face the daunting task of trying to get a result at a side expected to challenge for the title, so his plan could well backfire. However, the new boss was damned if he did and damned if he didn't. There were even suggestions from some West Ham fans that Bilic wasted his time even going out to Romania and should have stayed home and concentrated on the build-up to the Arsenal match. But that would have led to negative headlines either way and left supporters and the young side he put out feeling somewhat disenchanted and shortchanged. If he had sent the first team to Romania, they would have been in no fit state to face the Gunners and it would have implied that Europe was the priority for the Hammers. His policy showed exactly where his intentions are this season, at least he was brave enough to make a clear decision though.
4) Modibo Maiga has NO FUTURE at West Ham United... AGAIN
Earlier this week, West Ham co-owner David Gold said, on the Hammers’ official website, the club has the squad to cope with the injuries to Enner Valencia and Andy Carroll. Well if Gold seriously believes they can get by with the likes of Modibo Maiga in the team, West Ham are in for a long, hard season. Yet again he was inexplicably given another chance to impress and rescue his ailing career, but yet again he was truly awful. His work rate, touch, awareness, willingness to make space and look for the ball were dismal. The African was upstaged by the desire and professionalism exhibited by youngster Elliot Lee who was given no help by his striker partner, whose job it was to hold the ball up or flick it on to bring him into play. Maiga is making Titi Camara look like a good signing at this rate and now West Ham are out of Europe, surely he has played his last game in the claret and blue. If West Ham's owners go into the last season at the Boleyn Ground with the likes of Maiga up front, they are well and truly short changing the club's loyal fans.
5) West Ham did not deserve to be in Europe and it showed
The Hammers really had no right to be in Europe in the first place given that they finished 12th in the Premier League last season. The FIFA Fair Play rankings have now been deemed too farcical to offer qualifying places to teams topping them and from this season will be defunct. The east Londoners were the first Premier League side to be back in competitive action after qualifying for Europe through the backdoor fair play route. And they are the first to be eliminated as they ironically picked up a sending off in each round to scupper any hopes of a European adventure. Even the most ardent Hammers fan will concede they had little right to be in the competition, as nice as it would have been to see some big European nights under the lights at the famous Boleyn Ground for the last time. In a week, I have a feeling all this will be forgotten and the club, players and fans will have made peace with their short stay in a competition that could potentially have added as many as 23 matches to their schedule in what is one of the most important seasons in the club's history.