The Hammers blew away their opponents in the second half of Saturday afternoon's clash at the John Smith's Stadium, thanks largely to the work of attacker Marko Arnautovic.
United boss Moyes reserved special praise for Arnautovic at full time, with the Austrian playing a part in all four of his side's goals, before then turning attention to transfer activity heading into the second half of the January window.
"I'm really pleased with Marko," he told reporters. "Everybody knew how good he was at Stoke City and maybe giving him a freer role up front has given him a chance to express himself.
"The board know - and they want to add a few players - it's just the difficulty of the month. We want to add players if that is possible. We have a long way to go but the players have done brilliantly well since we came in and they did very well today."
Asked about his own personal landmark achievement of 200 top-flight wins, Moyes added: "To be in that position, alongside those great managers, is good and I'm just glad I have managed to win a few."
West Ham have now won eight points in their last four Premier League away games - as many as they managed in their previous 15 combined.