Boss Slaven Bilic added: “A couple of minutes before the goal we had a good counter with Marcus Browne but unfortunately we missed the target.
“Instead of 2-0, and probably killing the game, they get a corner and score.
“It is a good result. We played with some young kids and it was a great experience for them.”
West Ham were shocked by Astra in the final qualifying stage last year to miss out on the group stages.
Astra haven’t even got a manager as boss Marius Sumudica is currently serving a six-month ban from football, handed out in March, for placing bets on matches.
And their tiny ground only has stands on three sides.