Fearing something similar happening to Tom Cleverley, who was also on a yellow card, Ferguson withdrew his midfielder.
The Scot said: "I think Jack Wilshere was warned for his third foul on Van Persie then Thomas did a foul on Wilshere and I think he got warned.
"I wasn't prepared to take a chance and Anderson actually changed the game a bit for us."
England midfielder Wilshere had been in just his second match back after returning from a 14-month injury lay-off.
"His game is commitment. I will have to see the game but it didn't look to me like he went on purpose over the ball."