Arsene Wenger was left paying a heavy price for Arsenal reaching the Carabao Cup semi final.
Olivier Giroud hobbled off with a hamstring injury which is expected to keep him out for the Christmas fixture schedule and up to three weeks.
Arsenal striker Danny Welbeck hit the 42nd minute winner in an instantly forgettable cup tie but the two-legged semi final does leave Wenger facing a gruelling schedule of ten games in 36 days.
Wenger said: “Hamstring, normally 21 days.
"It looks like he (Giroud) is out for Christmas. We will normally do a scan 48 hours after – Thursday - then we will have an idea of the grade. When you hear him the pain is quite big but the grade is not always linked with the pain.
“It’s a very demanding run. We have already a tough schedule behind us, we have to sit down and analyse very well what we can do.
“What is very worrying in my job is when you start to lose players. Like Giroud. You can't afford to lose another one or another one. I have to look at how I manage the schedule.
“But it was a positive night apart from losing Olivier Giroud. I felt we played with quality and spirit and pace.
"Over the 90 minutes we looked very solid defensively. We were tested but not in danger.”
Arsenal made 11 changes, fielded fringe players and kids but were not tested because, incredibly, West Ham did not manage a single shot on target and Hammers boss David Moyes admitted he was frustrated with his side’s performance as they went out with barely a whimper.
Moyes said: “Disappointed with overall performance. But I think we are making steady progress. We have conceded one goal to Arsenal in two games and, when I came into the club, I might have taken that.”
But Moyes will be well aware that one player who is going backwards is Joe Hart, who has lost his place at West Ham, is in danger of losing his England No1 spot and will have to wait for the FA Cup now they are out of the League Cup.
Hart should have done better on Arsenal’s goal after 42 minutes. Francis Coquelin spread the ball wide, Mathieu Debuchy headed the ball back across and Welbeck charged in to bundle the ball home while Hart failed to command his box and West Ham’s defenders were also slack.
It just about summed up a scrappy game.
Gone are the days of fiery London derbies, big cup quarter finals and even the fans stayed away with an attendance of 44,741 because the match was not included in season tickets. Apathy reigns at the Emirates.
Theo Walcott missed the only other chance of the game, Giroud hobbled off after pulling his hamstring late on as he tried to spring forward and not even the introduction of Andy Carroll, Diafra Sakho and Marko Arnautovic could give West Ham extra bite up front.
This will be Wenger’s seventh League Cup semi final and yet it is the only domestic trophy he has not won. Maybe, just maybe, it might be his year.
PLAYER RATINGS
Arsenal: Ospina 6; Debuchy 6, Chambers 6, Holding 7, Kolasinac 8; Coquelin 6, Willock 6, Elneny 6, Walcott 6, Welbeck 7; Giroud 6 (Nelson, 78).
Substitutes: Reine-Adelaide, Akpom, Da Silva, Macey, Nelson, Nketiah, Sheaf
West Ham: Hart 5; Cresswell 6 (Sakho, 65), Reid 6, Collins 6, Ogbonna 6, Masuaku 6; Rice 6, Obiang 6, Quina 7 (Arnautovic, 83), Ayew 6; Hernandez 5 (Carroll, 65, 6).