The 'Better Than I Know Myself' singer and Koskinen were arrested in Helsinki earlier this week after engaging in a reportedly violent row at the bar.
Lambert later laughed off the matter, posting on his Twitter page: "Jetlag+Vodka=blackout. Us÷blackout=irrational confusion. jail+guilt+press=lesson learned. Sauli+Adam+hangover burgers= laughing bout it. :)"
However, he has since confessed that he feels "embarrassed" by the incident, and insisted that it was blown out of proportion by the press.
"Violence is not to be taken lightly. Embarrassed by drunkenness. No punches thrown, no injuries and no charges. Media always exaggerates," he wrote on the social networking site on Thursday.
Lambert recently discussed his fashion inspirations, saying that he finds beauty in "tacky" clothing.
Listen to Adam Lambert's 'Better Than I Know Myself' below: