David Moyes' side had already qualified top of their group and can look forward to a knockout game in 2022.
Moyes took the opportunity to make 11 changes to his side, with plenty of academy players getting a chance in the first team.
Before kick-off, Declan Rice said: "What a great night for the academy! Let's go boys."
There were five full debuts in the starting line-up for the Hammers, while Mark Noble's midfield partner Sonny Perkins was just a few months old when the legend made his first appearance for the club.
West Ham's rookies found themselves a goal behind after only three minutes, Mislav Orsic curling in a stunning strike from the left of the penalty area.
Orsic scored a brilliant hat-trick to dump Tottenham out of the competition last season.
The Hammers youngsters kept the game tight without creating many opportunities for themselves.
Said Benrahma was introduced at the break and gave a spark to the attack, but Moyes' side could not find an opening.
A few more youngsters were brought on to be handed their first experiences of football in a West Ham shirt.
The Hammers ended top of their group having won their opening five games and it was a tall order for the weakened side to carry that on, but equipped themselves well.