Craig Levein's side controlled much of the match in terms of possession, but lacked a cutting edge in front of goal.
Stephen McManus was unlucky not to grab the opener on 34 minutes when he knocked a volley wide of goal, while Kenny Miller headed straight at the home goalkeeper Zydrunas Karcemarskas moments after the break.
Miller's Rangers team-mate Steven Naismith had a couple of decent chances in the second period.
He saw Karcemarskas save on 58 minutes while he failed to get a shot away in the closing stages as Scotland pushed frantically for three points that would never come.
Lithuania's chances were few and far between. Saulius Mikoliunas clearly fouled Davie Weir on 16 minutes.
Weir, at 40, the oldest player to win a cap for Scotland, was floored by the home player but the referee somehow let play continue.
Mikoliunas pulled the trigger, but Scotland goalkeeper Allan McGregor was equal to the task as he stood upright to swat away the midfielder's shot.
Lithuania's best moment of the second period saw Tomas Danilevicius try to round McGregor before the hour mark, but Steven Whittaker was alive to clear the danger.
Lithuania spent most of the match defending in numbers. Mikoliunas was fortunate to avoid a yellow card after several late challenges on Alan Hutton and Barry Robson that characterised the home side's robust approach to the evening.
The home began with a 4-4-2 formation with former Scottish Premier League players Andrius Skerla of Dunfermline Athletic and former Hearts man Mikoliunas operating for them as Scotland opted for a 4-5-1 formation that saw Lee McCulloch deployed to protect the defence.
McCulloch was playing his first game since Scotland lost 2-1 to Italy in their closing match of the Euro 2008 qualifiers, but he had a decent match, even if Weir and Stephen McManus hardly needed protecting.
Weir strolled through the evening with his positional sense a joy to behold on his 65th appearance for his country.
Weir also became the oldest player to feature in a European championship game, eclipsing former Germany captain Lothar Matthaus, who was 39 when he played in the 2000 finals.
He is likely to be relied upon heavily by Levein in this campaign if he stays clear of injury.
The Rangers skipper was joined in the Scotland starting line-up by five of his club team-mates and that seemed to give the visiting side a strong spine.
All Scotland lacked was a goal and Miller wasted another opportunity with 11 minutes remaining as he got too much power on a header in attempting to direct it towards goal.
Scotland's other main downfall was their wastefulness from free-kicks. Barry Robson seemed to spend large chunks of the match either hitting the first man or floating the ball too deep before he departed to be replaced by James McFadden in the final 20 minutes.
Having failed to record a win in their opening group match, Scotland's home encounter with Liechtenstein at Hampden Park on Tuesday now becomes a night of some importance.
With world champions Spain, who won 4-0 in Liechtenstein, and the Czech Republic also in Group I, Scotland cannot afford to spill any more points against the so-called weaker sides in the section.