The actress passed away after hitting her head while skiing in Quebec, Canada in 2009, just days after she had watched Everett perform in New York play Blithe Spirit.
In his new memoirs, serialised in Britain's Daily Mail, Everett details his last meeting with Richardson, who played his lover in The Comfort of Strangers, backstage after the production.
He also recalls gathering around her open coffin with her ex-husband Robert Fox and her mother Vanessa Redgrave, writing, "We all look down into the casket, searching for life, but it only whispers round the rigid features."
Everett goes on to admit he and Richardson were not always close, and reveals regret for not spending more time with her when she came to see him on Broadway.
He adds, "The truth is Tasha and I gave one another a wide berth while she was alive. We knew each other well; but despite many connections and similarities, we didn't get along. Perhaps we were more alike than we cared to admit...
"I've plunged into a terrible depression... Tasha was holding out an olive branch to me (by coming to see Blithe Spirit), and it all went wrong. It's quite an effort, after all, to come and see someone in a show. Why didn't I ask her to dinner that night after the play?"