The former Motherwell boss, who has been working as a television pundit recently, said: "It's been a whirlwind. I've been quite gob smacked by the whole thing, even the media attention.
"It has been great - if a bit different. It was difficult going into the Arsenal press conference the other night and being booed by the English press men.
"That was quite a new experience - I never had that before.
"They've slaughtered me in the past but I've never actually been booed by them."
Butcher admitted he had to overcome some initial misgivings before accepting Burley's offer.
He said: "I did have some qualms about taking the job on.
"I had to speak to a lot of people and at certain times I thought, 'I don't think this is going to work' but then I spoke to more people about it both north and south of the border the more they convinced me.
"I spoke to George who is strong as both a manager and a character as well. I've spoken to a lot of people including ex-team mates and they are very pleased.
"My major worry was for George - not so much myself. I've had criticism and booing in my career and I'm not bothered about that but I didn't want to do anything which would hurt or jeopardise George.
"But he's very positive and has good thoughts for the national team."
Butcher added, tongue-in-cheek: "If Scotland lose I'll get all the blame, if Scotland do well then George will get all the praise, but I don't mind that."