Auri started his career in Lithuanian clubs FK Zalgiris Vilnius and FK Inkaras Kaunas, before he was bought by Danish Superliga club Brøndby IF in 1995, after he and FK Inkaras Kaunas met Brøndby in the 1995 UEFA Cup. At Brøndby he immediately won silverware, as the club won three Danish championships in a row in the 1995–96, 1996–97, and 1997–98 seasons. Despite only playing 17 games over the three championship winning seasons, Auri earned himself a cult following in the stands during his early years at Brøndby, as he didn't succeed in scoring any goals for the club. Apart from this, he was well liked for his high work ethics and team spirit.
Following the summer 2002 arrival of new manager Michael Laudrup, new player Asbjørn Sennels was bought for the left side of the defence in the following December. Sennels was a part of the Danish national team at the time, and even though Sennels initially didn't find his feet at the club, Auri played the rest of the season as a substitute for the left and right side of the defence. Auri spent the next few years mainly on the bench in Brøndby, and for the last half of the 2004–05 season he was put on loan at Superliga relegation battlers Herfølge BK. Herfølge ended the season with relegation, and Auri returned to Brøndby to collect his 5th Danish championship title for Brøndby, for the games he played in the first half of the season.
For the first half of the 2005–06 season Skarbalius only took part in 3 matches for a combined 72 minutes on the pitch, and his contract was mutually terminated of 31 December 2005 to allow Auri to become a playing assistant coach at Herfølge in the Danish 1st Division. Before leaving Brøndby he managed to become the most capped foreign player in the club's history with almost 200 appearances.
Skarbalius is a former captain of the Lithuania national football team, and he previously held the record number of appearances for Lithuania with 65 international caps, during which he has scored 5 goals. He retired from international football in October 2005 after spending all 14 years with the national team since Lithuania gained independence.
In November 2006, he was promoted to head coach of the Herfølge BK. When Herfølge in 2009 merged with Køge Boldklub, Skarbalius continued as manager of the new club called HB Køge. On 8 June 2011 it was announced, that Auri would be taking the job as assistant manager for Henrik Jensen at his former club Brøndby IF starting in January 2012, but when Jensen was sacked on 24 October, Auri was appointed as interim manager for the remainder of 2011.
In October 2012, with Brøndby last in the 2012-13 Superliga table, Skarbalius was expected to be sacked soon, according to Danish bookmakers. However he remained as head coach for the remainder of the season and on 20 May 2013 a new Superliga contract was secured in the last game away to Horsens. However, due to the disappointing season he was sacked on 10 June 2013 and replaced by Thomas Frank.
In September 2013 he was announced as manager of minor Danish club Haslev FC. He managed Haslev until Christmas 2013, and in February 2014 he was announced as the replacement for the knee injured Ove Christensen at Viborg FF.