The North West outfit suffered a 1-0 defeat at the hands of the Blues during a quarter-final replay at Stamford Bridge yesterday.
The centre-back returned to the United side for the clash following his omission from the team that secured a 1-0 victory over Sunderland in the Premier League on Saturday.
Ferdinand wrote on Twitter: "Gutted about the result yesterday. Real FAcup atmosphere, our fans were unreal. Just disappointed we couldn't send ya home happy."
While hopes of clinching the double have been thwarted, United are on course to secure the Premier League title due to their 15-point lead at the top of the table.