Terry, 31, was fined £220,000 and banned for four matches by the Football Association and he this week announced that he would not contest the ban.
In a statement this week, Terry apologised for his actions but did not directly address the QPR defender.
"The press mentioned quite a bit yesterday that Anton Ferdinand was not mentioned specifically in the John Terry apology. John Terry apologised to everybody and, in my mind, that should mean an apology to Anton Ferdinand," Buck told talkSPORT.
"In the criminal court, I sat a few seats away over the four days from Anton Ferdinand's family - his father, his mother and one of his siblings. I could see the effect it was having on them and it wasn't good.
"I understand, and as a club we understand, what they have gone through since a year ago. Chelsea football club would like to apologise to them. It's been a very difficult year for them and they didn't do anything wrong. They shouldn't be suffering and we're sorry."
Buck also revealed that Terry had been heavily fined by the club but would remain as captain of the Blues.