"I always try to lead by example but some people don't want to see that," the 27-year-old Chelsea enforcer told Serbian media on Saturday after a poor performance in Ostrava.
"The attitude of some players is unacceptable, not just on the pitch but off it too and it was obvious from the moment we got together on Monday.
"I told our coach (Radovan Curcic) there is no point in me carrying on with the national team if things don't change."
The Serbians failed to qualify for Euro 2016 after an awful campaign, having also missed out on the 2014 World Cup and Euro 2012.
The national team's managing director Savo Milosevic, a former Aston Villa striker, hinted that he and Curcic could pay the price for the barren spell.
"Reading between the lines of Curcic's statements after the Czech game, one could see that he is on the brink of stepping down and I am in the same boat with him," Milosevic said.
"I have asked for support and patience for the players in the past eight months but their lack of commitment is quite simply indefensible."
Matic cited Serbia's futile 2-0 win at bitter Balkan rivals Albania in their penultimate Euro 2016 qualifier, when they had already lost any hope of reaching the tournament, as an example of how they should move forward.
"When our personal reputations were on the line we did everything right," said Matic who has played 26 times for his country.
"But I'd really like to know whether some of my team mates apply the same poor working ethic at their clubs as they do in the national team most of the time."
(Writing by Zoran Milosavljevic, editing by Ed Osmond)
