Joe Cole had delivered a vintage display on his return to his boyhood club following a free transfer from Liverpool this week, setting up two James Collins goals to cancel out Tom Cleverley's opener.
But substitute Van Persie scored a stunning injury-time equaliser from a superb cross-field pass from fellow substitute Ryan Giggs to force a replay at Old Trafford.
Manager Ferguson told MUTV: "We missed some good chances, with headers over the bar and (Shinji) Kagawa had one blocked on the line, I thought it was not going to be our day.
"But you have to say the pass from Ryan Giggs, then the first touch from the ball from Robin and his finish was world class."
Ferguson was delighted to have made sure they did not suffer a disappointing early FA Cup exit.
The United boss continued: "We want to stay in it and have a go at it this year.
"We have had some terrible draws over the years and been knocked out early and we don't enjoy that."