United produced yet another commanding and confident display on the road to see off Sam Allardyce's Hammers side. However, Moyes did feel that a bigger winning margin would have been more reflective of the Reds’ dominance over the course of the 90 minutes.
Reflecting on the overall result, Moyes said: "I thought we played very well. The disappointing thing is that we didn't take more of the chances we created in the first half. I think Shinji [Kagawa] had a chance, Juan [Mata] had a chance and [Marouane] Fellaini could probably have scored with a header early on. I was a little bit worried when we missed those opportunities as to how it was going to be, but we thoroughly deserved the win."
Injuries and suspension forced the manager into several alterations to his team that earned a morale-boosting win over Olympiacos in midweek, but the performance of Michael Carrick in central defence also pleased the boss.
"Being an old centre-half myself, I thought he made the job look easy," he added. "I felt like saying to him that it's easy playing centre-half and he was terrific. West Ham had opportunities because they are a handful, but between him [Carrick] and Fellaini I thought they dealt manfully with Andy Carroll."
Moyes is now hoping that this win, coupled with the confidence from the victory over Olympiacos, can help spur his side on to the challenge posed by Manchester City's visit to Old Trafford on Tuesday. "You can never refer this game to the next one but all we want to do is get a bit of momentum and that's something we haven't had an awful lot of," he said. "Hopefully we can go into Tuesday's game showing a bit more confidence. The midweek game helped and today's performance will help as well."
More: Report: West Ham 0 United 2 | Video: Hammers highlights