Former England captain Terry came face-to-face with Bernstein at a ceremony where Chelsea handed the UEFA Champions League trophy over to the City of London ahead of May's final at Wembley.
Bernstein greeted other players from the Chelsea squad at the ceremony at Whitehall, but Terry appeared to snub the chance to shake hands or speak to the FA chairman.
There has been an uneasy relationship between the pair since Bernstein stripped Terry of the England captaincy last year over the Anton Ferdinand race row.
Asked what his relationship was like with the FA and if he shook Bernstein's hand, Terry told Sky Sports News "No, listen, it's a difficult one for me. Obviously he went and spoke about me in the court case and I don't want to talk on it.
"It is probably a subject we should maybe just avoid."
Bernstein failed to recognise he had been snubbed by Terry.
"I didn't even notice that," he said. "I didn't notice anything.
"My relationship with everybody in here is really fantastic, I didn't notice a thing. I think we should talk about more positive things than that sort of nonsense."
Asked how he would describe his relationship with Terry, Bernstein admitted: "A little distant."
Pushed on could the relationship be repaired, Bernstein added: "I don't know, I am not really terribly concerned to be absolutely honest.
"I have got other things to think about in my last three months, I have other priorities."