The Scots looked solid and comfortable in possession but they failed to find the breakthrough despite some decent opportunities.
Barry Robson forced several saves from long range, Kenny Miller headed straight at the keeper from 12 yards and Steven Naismith lacked conviction when presented with a shooting chance on the edge of the box.
Levein prompted some raised eyebrows when he named his team on the eve of the game with Naismith preferred to James McFadden in left midfield.
The move was part of a plan to designed to give Scotland a more solid look following last month's 3-0 friendly defeat in Sweden. Levein certainly succeeded with that aim after making eight changes and bringing back experienced players such as Lee McCulloch, Stephen McManus and 40-year-old Davie Weir, who became Scotland's oldest capped player.
But his team lacked a clinical edge despite dominating possession in Kaunas against a side who were missing injured Hearts skipper Marius Zaliukas.