Smith, boss of the national team between 2004 and 2007, was linked with the post after the departure of Gordon Strachan in October.
However, McLeish was named manager for the second time last month and is preparing for the friendly against Costa Rica at Hampden Park on Friday night before another clash against Hungary next Tuesday.
Smith, 70, said: “I never got to the stage where, despite what you might have read, the SFA (Scottish Football Association) offered me the job. They only asked if I would be prepared to come out of retirement and that is effectively where it was.
“I suppose there is always a little bit of a pull to come back again but, in the end, I felt I had been out for too long a period and happy enough to get my golf handicap down which I am failing to do.
“Alex McLeish is a tried and tested manager. If anything, he is one that we should have gone for in the first place.”