Stojanovic stepped down after one year in charge during which Slovenia managed just three points from four matches in European qualifying Group E.
"We have failed to live up to our own expectations and wishes in the 2014 World Cup qualifiers and I feel responsible for the results," Stojanovic was quoted as saying by the NZS.
"I wish the team the best of luck and success in the future and I also want to thank the NZS for giving me the opportunity to work with the national team."
Slovenia's next match is at home to Iceland on March 22. Switzerland top Group E with 10 points from four games, followed by Norway on seven. Albania and Iceland have six each while Slovenia and Cyprus are a further three points adrift. (Reporting by Zoran Milosavljevic in Belgrade; Editing By Alison Wildey)