The Scottish Football Association (SFA) has resumed its search for a new boss after Northern Ireland manager Michael O’Neill turned down the chance to replace Strachan, who departed following failure to reach this summer’s World Cup.
Edinburgh-based O’Neill held talks with the SFA last week but on Monday decided against the move to Hampden Park.
Asked on talkSPORT if it had to be a Scot to run the national team, Strachan said: “It is meant to be a Scotland team so Scotland players, a Scotland coach, I prefer it that way.
“Same with England, same with Ireland, Wales as well, that is your national team so that’s the way I would go, unless you are a country that is developing in football that you need a coach to help you along.”
Strachan, who admitted his departure from Scotland “is still raw, it still hurts”, was not totally surprised by O’Neill’s decision to stay with Northern Ireland.
The former Coventry, Southampton and Celtic boss said: “When I met Michael first of all when I started coaching him at Coventry, he always asked questions, always willing to take information but at the end of the day he was his own man.
“There was a lot to be thinking about, a lot to be done - he lives in Scotland and he could have been swayed by emotion - but he has had a look at it and for whatever reason, I don’t know, he has decided to stay with a group of people that he has worked very well with for the last five years, he knows the people there.
“Sometimes you get so long to think, there is so many things come into your thinking and you think well, it seems like a good idea at a time but the longer you have to think of it you think maybe it is not such a good idea.”