Vancouver Whitecaps frontman Miller announced he had played his last game for his country last week after winning his 69th cap in the 3-2 friendly defeat to England.
But the former Rangers, Celtic and Hibernian attacker signed off on a high as he bagged his 18th goal for Scotland at Wembley to leave him sixth on Scotland's all-time list of top scorers.
And Levein - who was sacked as Scotland manager after the team's dismal start to the current World Cup qualifying campaign - believes Miller timed his decision just right.
He said: "I was up off my seat when he scored against England but I think Kenny has picked the right time to go.
"I know he always said he would never retire but he has been a brilliant servant to Scotland.
"He has travelled a long way to play for the national team, especially since he has moved to Canada, and that is not easy when you get a bit older.
"But I have nothing but admiration for him and hopefully he can play the last couple of seasons wherever he wants to and then drift off into the sunset."
Levein was axed by the Scottish Football Association in November after the Dark Blues opened their Group A by failing to win any of their first four matches.
But he says he is now ready to re-enter management.
The ex-Hearts, Leicester and Dundee United boss said: "I'm desperate to get back into management. I found after my Leicester experience that I came back a better manager and I'm convinced I will do so again, whenever the right opportunity arises.
"I've had bits and pieces in terms of offers but nothing concrete yet."