Van Persie scored from the penalty spot on his return to North London as United came from behind to earn a point in a 1-1 draw at the Emirates Stadium.
Ferdinand believes that Arsenal fans must grudgingly accept Van Persie's reasons for moving last summer in search of a maiden Premier League title.
He told The Sun: "Robin conducted himself the way we expected him to. He's a classy guy and he did well.
"You have to understand that fans are going to have their opinions and they are going to voice them. He didn't come here unaware that people were going to be resentful.
"When they go home and take stock of what he's achieved this season, he has come in and won a trophy in his first season. That was his aim and that was the reason why he came to us. In the cold light of day, the Arsenal fans will understand."
The 29-year-old leads the Premier League scoring charts in his first season with United after taking his tally to 25 goals at the Emirates.