The 30-year-old England skipper issued a statement after video footage was posted on the Internet.
"I'm disappointed people have leapt to the wrong conclusions about the context of what I was seen to be saying to Anton Ferdinand," Terry said. "I thought Anton was accusing me of using a racist slur against him.
"I responded aggressively, saying I never used that term. I would never say such a thing and I'm saddened people would think so."
Terry said there was no problem between him and Ferdinand when the pair spoke after the game which Chelsea lost after being reduced to nine men in the first half.
"I congratulated him on their win. He has not accused me of any wrongful remark," Terry added. "It was clear it was all a misunderstanding at the time.
"After the result today I am saddened to be dealing with these wrongful allegations.
"I am the proud captain of one of the most internationally diverse teams in the Premier League and I absolutely believe there is no place for racism in sport and indeed in any walk of life."
Last week Manchester United defender Patrice Evra accused Liverpool striker Luis Suarez of racially abusing him in their 1-1 draw at Anfield.
The Uruguayan has denied any wrongdoing and the Football Association is investigating the matter.
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