The Premier League outfit got the better of Maltese side Birkirkara in the second qualifying round, but only on penalties.
The Hammers won the first leg of the tie 1-0 at the Boleyn Ground and lost the second leg in Malta by the same margin on Thursday.
The tie went into a penalty shootout, which West Ham clinched 5-3 to retain their chances of featuring in the group stage of the 2015-16 Europa League campaign.
Following the narrow victory, goalkeeper Adrian, midfielder Poyet and forward Zarate took to Twitter to send a message to the West Ham fans.
Nobody said this would be easy...of course we need improve but the most important is to improve winning games.Next round!#EuropaLeague— Adrián San Miguel (@AdriSanMiguel) July 24, 2015
Yesterdays game is now in the past, now we have to improve for our next game in the Europa League. Thanks to everyone for the support.COYI— Mauro Zarate (@mau_zeta) July 24, 2015
Difficult night yesterday but we're through and that's all that matters in the end.Happy to have played a part and well done to all the boys— Diego Poyet (@diegopoyet7) July 24, 2015
Big thanks to everyone for their kind messages and for those who came to support us in Malta. Big game next week at our place COYI— Diego Poyet (@diegopoyet7) July 24, 2015
West Ham will face FC Astra Giurgiu in the third qualifying round of the Europa League.
Astra saw off Scottish Premiership side Inverness Caledonian Thistle 1-0 on aggregate in the second qualifying round, and will provide a tough challenge for Slaven Bilic’s side.