The Chelsea captain confirmed to Sky Sports News that he had rejected Bernstein's attempt to shake hands.
Bernstein was the man who stripped Terry of the England captaincy after his racism charge. Terry is also unhappy with Bernstein's role in his court case last year where he was cleared of a racism offence though later banned for four matches by the FA.
Terry said: "It's a difficult one for me - he went and spoke about me in the court case."
Asked if he shook Bernstein's hand, Terry replied: "No."
Bernstein insisted he was unaware of the Chelsea player's snub when quizzed on the matter by Sky Sports News.
"I didn't notice anything," said Bernstein, who will stand down from his role in July. "My relationships with everyone here are really fantastic. I didn't notice a thing and I think we should talk about more positive things than that sort of nonsense."
Asked about his relationship with Terry, Bernstein admitted they were "a little distant" but seemed cool on making any attempt to build bridges when asked if there was any hope reconciliation.
"I don't know," he said. "I'm not really terribly concerned.
"I have other things to think about. In my last three months, I have other priorities."