The Red Devils were 3-0 down just five minutes into the second half of the Premier League match but came back to draw 3-3 thanks to two Wayne Rooney penalties and a header from Javier Hernandez.
And the United centre back, whose brother Anton is at the centre of the John Terry row after accusing the England man of racially abusing him, was booed throughout the match.
However, the defender later hit back via Twitter, commenting: “I got booed by the CFC fans today — well done guys. Thanks for inspiring me & the lads!
“That's like fuel to me! TeamSpirit.”
Chants of “Rio Ferdinand, your brother is a c***,” were alleged to be heard at Stamford Bridge in an unsavoury a show of support for Terry, who was absent due to injury, following the incident in October.
The FA recently stripped Terry of the England captaincy, against the wishes of manager Fabio Capello, after the centre-back’s trial was delayed until July 9, after the Euro 2012 finals.
Blues manager Andre Villas-Boas said: "You have to condemn it when there is discriminatory, aggressive behaviour but you don't expect opposing fans to cheer your players."