The striker scored the opening goal for the Saints before setting up Dusan Tadic for the visitors' second as they got the job done at the London Stadium.
"It's a massive result to come away to West Ham and win 3-0. We're delighted with the performance and we've got the keep this run going," told the club's official website.
"It's four wins on the bounce so we're going into Thursday (Europa League at Hapoel Be'er Sheva) now all guns blazing!
"In the first ten to fifteen minutes we stepped off and showed a bit too much respect maybe but when we got a foothold we were deserved winners."
Austin also feels playing up front in Claude Puel's creative and free-flowing team is a delight in itself.
"You're delighted as a striker as you just want to score goals," he added.
"That's what you're credited on but for look at the team we've got, we're always going to create chances so it's a dream!"