Rooney missed the 3-3 draw at Goodison Park following newspaper revelations about his private life.
The England striker and wife Coleen this week asked for privacy while they sort out their private life, and Ferguson said before Saturday's game: "We made a decision simply because he gets terrible abuse here. We don't want to subject him to that."
Beckham has backed his former boss to handle the situation in the right way.
"Sir Alex Ferguson knows more than me and definitely knows more than anyone about his players," Beckham told Sky Sports News.
"He has obviously made a decision what is best for for him and for his team."
"He's definitely being looked after by the right club and the right manager and with the right people around him.
"He's a great footballer at the end of the day."
Rooney and his wife released a statement on Friday saying the "last six days have been extremely painful for us and for our families".
The couple have faced a week of torrid speculation and newspaper headlines after claims the Manchester United striker visited a £1,200-a-night prostitute while his wife was pregnant.