McGhee, who was sacked before Christmas at Bristol Rovers and endured a torrid time as manager of Aberdeen, said: "I see those two episodes as failures. I feel unfulfilled as a manager, so I still have things to do."
McGhee said he had no hesitation in accepting Strachan's offer of a job but added: "I have questions to answer and I think I can only do that below the surface.''
He hoped the Scotland job could give him a sense of achievement. "I think you have to be determined and I feel very unfulfilled as a manager, regardless of the successes that I have had, and I have had a lot of successes,'' he said.
"I imagined that I would spend my whole life managing in the Premier League and I haven't, so I still have things to do and getting an opportunity at this level is okay."
McGhee also refused to dismiss the rest of the qualifying campaign for the World Cup in Rio as a forlorn cause.
He added: "It seems like it has almost been totally written off. I am far enough away maybe not to fully appreciate the gravity of the situation but I think with six games to go there surely must still be hope."