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The Dutchman failed to find the net in United's victory at the Hawthorns and appeared fortunate to escape a red card early in the second half.
Van Persie was first cautioned for scything down Morgan Amalfitano from behind before making a late challenge on Steven Reid a matter of moments later with United still only one goal in front.
"I thought it was a foul, but it did not warrant a yellow card," Moyes told MUTV.
"I was always taking him off anyway because he played 90 minutes for Holland in midweek.
"I actually told him in the hotel that I'd try to get him off at the right time in the game, so it made the decision easy. I couldn't afford him to have another challenge and give the referee a decision to make."
Wayne Rooney followed up Phil Jones' first-half opener with his 11th Premier League goal of the season, before setting up substitute Danny Welbeck - who came on for Van Persie - to round off the scoring late on.
"I thought Robin and Wayne were excellent - [Juan] Mata and Adnan [Januzaj] too," he added.
"But we also needed a good defensive performance as well, so, all round, I'm pleased.
"The pitch was very lively; it was drying out a little bit and it wasn't that easy to pass the ball, but we looked much more potent going forward and looked more likely to score than we have in other games.
"I made the point about us trying to attack more and have better play going forward and I think we did that."