Manager Slaven Bilic said he was “angry and frustrated” after West Ham failed to reach the Europa League group stage.
The injury-hit Hammers lost to Romanian champions Astra Giurgiu in the qualifying round for the second season in succession.
The visitors won 1-0 in Thursday’s second leg at the London Stadium to go through 2-1 on aggregate.
“I’m not going to lose faith in the players after one game,” said Bilic. “We’re missing top-quality players.”
Former West Brom and Barnsley midfielder Filipe Teixeira’s precise first-half finish secured victory for Astra as West Ham failed to convert any of their 17 attempts at goal.
“The disappointment is massive,” said Bilic. “We didn’t play good in the first half or with desire as a team. We were second best.
“I’m angry and frustrated but I’m much more disappointed than anything else.”
Bilic made eight changes from Sunday’s Premier League win against Bournemouth, although he had few attacking options with Dimitri Payet, Andy Carroll, Manuel Lanzini and Andre Ayew injured.
Bilic has said he is interested in signing Manchester City striker Wilfried Bony, while West Ham announced the arrival of Swiss midfielder Edimilson Fernandes from FC Sion before kick-off.
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