The Tartan Army coach was pleased with his side's performance in Larnaca, highlighting the class of the goals but warning about their failure to retain possession
In an entertaining game, the Tartan Army came out as deserved winners thanks to the Cardiff City striker's stunning goal and the QPR forward's composed finish.
The 47-year-old coach applauded Miller's work in training and stated he was delighted for Mackie to be back after recovering from a broken-leg suffered last season.
He told the BBC after the game: "The first [goal] is fantastic for us, because it's something Kenny's been working on.
"The second was a fantastic piece of skill by Jamie Mackie. He's been out for a long time and I'm thrilled for him to get back into the team and score a good goal."
Levein's side played very well at times and could have scored more than the two goals they got, however the boss warned his side that they need to be more careful in possession.
He added: "I think we played well, exceptionally well on occasion.
"I felt we were a little bit too careless in possession at times and as a result of that I think we gave up too many chances. I certainly would have felt more comfortable had we kept better possession of the ball at times."
Scotland were subject to a slow start, waiting until the 24th minute to make the breakthrough, but Levein maintained that he was pleased with the game.
He said: "International football isn't about going at 100 miles an hour, it's about retaining possession of the ball and waiting for your time to make opportunities and score goals.
"We had some good chances early on. I was happy with the way we passed the ball and created opportunities.
"They had a couple of shots from distance that troubled us, but in general I think we deserved to win the match and overall I'm pretty pleased for the guys."