Nigerian international, Victor Anichebe, and his West Brom Albion side suffered a 3-0 defeat in the hands of Manchester United at the Hawthorns on Saturday.
Moyes wrote to United supporters earlier this week thanking them for their patience during what he admitted was a far worse debut season than he ever expected.
Phil Jones headed United ahead before Wayne Rooney scored his 13th of season after the break.
United rarely looked in trouble and substitute, Danny Welbeck, rounded off the win, which moved Moyes’ team up to sixth in the Barclays Premier League.
Anichebe caused panic by charging down Jones’ early attempted clearance, but Patrice Evra came to the rescue.
The Nigerian charged at the United defence again, but Chris Smalling did just enough to push the striker wide.
United started to take a hold of the game around the quarter-hour mark, with Juan Mata and Adnan Januzaj pinging dangerous crosses into the box.
Januzaj earned a couple of yards on his marker with a sequence of step-overs and he found Rafael at the back post.
The unmarked Brazilian headed towards goal but Foster tipped his effort on to the bar and West Brom cleared.
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