Lausanne - Croatia on Thursday were deducted one point from their Euro 2016 qualifying campaign after a swastika was scrawled on the pitch ahead of the 1-1 draw against Italy in June, UEFA confirmed.
After the penalty Croatia are on 13 points at the top of Group H, with Italy second, one point behind.
UEFA also ruled that Croatia's next two home matches will be played behind closed doors and have banned the team from playing qualifiers at the Split stadium where the incident occured.
They were also hit with a 100,000 euros ($110,000) fine, but escaped a ban.
Croatia have three days to appeal the ruling.
The swastika on the pitch at Split was removed by groundsmen at half-time of the draw between Croatia and Italy on June 12.
The Croatian federation apologised for the incident which they said "brought prejudice against football and the Croatian State and labelled it an act of sabotage".
Last month Croatia's Prime Minister Zoran Milanovic had pleaded with UEFA not to expel his country from the European Championships because of a swastika scrawled on the pitch used for an internatioinal.