Walcott criticised Capello in his new book.
The Italian said: "I was speaking to him at Arsenal. I said, 'I prefer you as player than a writer'. He smiled and then scored a goal!"
Capello says that Walcott knew his threat to "kill" him was lighthearted.
"It was a joke," Capello insisted. "He understood the joke.
"In my life. I respect all people. You respect me, I respect you. There are different rules - you are the player, I am the manager. It's normal.
"When I speak with the players at the start of the season I always said this, 'My role is to be manager and your role is to be player. I respect you and you need to respect me'. This is important. I told him this."