Cornell, who was the founder-vocalist of bands such as Soundgarden and Audioslave, committed suicide by hanging.
In a letter acquired by Billboard, Vicky wrote, "I'm sorry, my sweet love, that I did not see what happened to you that night. I'm sorry you were alone, and I know that was not you, my sweet Christopher. Your children know that too, so you can rest in peace."
She added that although she is "broken", Vicky said she will stand up for him and will take care of their children - daughter, Toni (12) and son Christopher Nicholas (11).
The "Black Hole Sun" singer was cremated on Wednesday at the Hollywood Forever Cemetery.
Cornell was found dead in his hotel's bathroom, an hour after wrapping up his concert in Detroit's Fox Theatre on May 17.