The home side narrowly avoided their worst ever international result with a stoppage-time winner from Stephen McManus in their 2-1 triumph in Tuesday's match at Hampden Park.
However, the SFA's acting chief executive George Peat has said sorry to their opponents for the abuse directed at the Liechtenstein national anthem, which has the same tune as England's anthem 'God Save the Queen'.
Peat said: "I was embarrassed and extremely disappointed by the disgraceful behaviour of some of our supporters during the Liechtenstein national anthem at Hampden Park last night.
"The Scotland fans have worked hard to earn their reputation throughout the world as fun-loving and respectful followers of football. Last night, those who chose to boo our opponents' anthem, only served to tarnish that reputation.
"I apologise unreservedly to our visitors for the crass reaction to their anthem, just as I did in private last night to the Liechtenstein delegation.
"It must not be forgotten that all nations must abide by FIFA's Fair Play policy and last night's behaviour does nothing to help Scotland's image."
