Van Persie was on the periphery of matters throughout United's routine 3-0 victory at The Hawthorns on Saturday, and appeared fortunate to escape a red card when he seemed to let his frustrations get the better of him early in the second half.
The Dutchman was first cautioned for scything Morgan Amalfitano down from behind, before then making a crude, late challenge on Steven Reid a matter of moments later with United still only one goal to the good.
Referee Jonathan Moss opted for a stern talking-to instead of producing a second yellow card, and Moyes substituted the striker soon after.
However, Moyes said Van Persie's withdrawal had been decided upon pre-match and did not feel his tackle on Reid was worthy of another caution.
"I thought it was a foul, but it did not warrant a yellow card," the Scot 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."
United's much-vaunted front four of Van Persie, Wayne Rooney, Juan Mata and Adnan Januzaj all started at The Hawthorns, and produced a more cohesive display as they continue to gel as an attacking unit.
Rooney followed up Phil Jones' first-half opener with his 11th Premier League goal of the season, before then setting up substitute Danny Welbeck - who came on for Van Persie - to round off the scoring late on.
Moyes was happy with the performance of his forward line, while also reserving words of praise for his defence.
"I thought Robin and Wayne were excellent - Mata and Adnan 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."
