Farbrace, who moved from Sussex at the end of the season, has not yet officially started in his new role at Lancashire but delivered the news to Anderson at a meeting last week alongside chief executive Richard Kenyon, who has also recently been appointed.
The news was first reported on Wednesday and Lancashire did not comment officially until Sunday. At a meeting with members on Monday, the club said they would look into arranging Anderson a farewell .
"It shows a lack of leadership at that club," said Broad, whose combined total of Test wickets with Anderson stands at a record 1,039 in 138 Tests.
"It shows a lack of doing it the right way.
"Paul Farbrace is new, but where is the chair?…