Tomas Soucek scored the only goal for the Hammers.
Ramsdale was back in goal for the Gunners as they progressed in the Carabao Cup.
For some footballers at the highest level, the early rounds of the League Cup can represent something of a chore. This time last season, that might have been the case for Aaron Ramsdale. This year, though, a midweek trip to Brentford represented an enormous opportunity for the England goalkeeper.