"That was the clincher," academy manager Westley, who stood in for Slaven Bilic, told the club's official website.
"We got one goal and made it virtually impossible for them.
"The one real opportunity Elliot got, he showed some class and finished it really well. He worked tirelessly on his own, as he was up there completely on his own after about ten minutes.
"All credit to him, and to Morgan (Amalfitano) and (Matt) Jarvis in the wide areas and Diego Poyet and Josh Cullen in the middle. They had to work hard because we only had ten men."
West Ham won the two-legged tie 4-0 on aggregate to move through to the second round of qualifying where they will take on Maltese club Birkirkara starting next week.