The Hammers raced into a 2-0 lead on the south coast, Michail Antonio opening scores on five minutes before Lucas Paqueta grabbed a second seven minutes later.
Declan Rice made it three shortly before the break, with Pablo Fornals confirming the result on 72 minutes with the fourth and final goal.
Despite his side’s relative control of the scoreline, Moyes shared that he had not counted his chickens before they had hatched, pointing towards recent comebacks in the Premier League.
Last weekend Hammers came from two behind to draw with league leaders Arsenal, whilst the Gunners themselves overcame a two-goal deficit to draw 3-3 with lowly Southampton“It was an excellent win.
Asked about Fornals’ goal,
David Moyes replied: “I was just thrilled we got it. Because even at three, if they get a goal – more so than ever, we are seeing teams coming from comebacks and we were 2-0 down last week. We saw Arsenal Southampton, 3-1 and a comeback, you never know at the moment how these things are going.”
Cherries head coach Gary O’Neil shared after the game that Moyes had told him he felt the 4-0 margin flattered West Ham, with the Hammers boss believing his side to have been “clinical” with their opportunities.
Gary O Neil said: “I thought Bournemouth put us under pressure, had a few opportunities. We were clinical when we got our opportunities. We got off to a great start in the game and especially after the midweek game, it gave us a real lift. I thought the players went into the game with a lot of confidence and self-belief from reaching another semi-final and obviously we had a really good comeback against Arsenal last week. We defended the box very well. I didn’t like that we gave up so many opportunities. We did that part when we had to as well. I thought Bournemouth had opportunities as well.”