The executive committee of European football's ruling body also called for tougher sanctions on Thursday, hours before a European fans' monitoring group, Fare, said it sent FIFA reports of "racist or xenophobic abuse" at three World Cup qualifiers.
FIFA President Sepp Blatter has also called for stricter penalties, and his governing body must now decide on opening disciplinary cases into incidents last Friday at Croatia vs. Serbia, Poland vs. Ukraine and San Marino vs. England.
England fans reportedly chanted songs about Manchester United defender Rio Ferdinand and his brother Anton, who are black.
Rio Ferdinand declined to join the England squad last week after being selected, and his brother was involved in a high-profile case that led to Chelsea captain John Terry being suspended for four matches for racial abuse, and losing the England captaincy.
During that case, Chelsea was criticized for how its officials and players supported Terry, including providing witness statements in his defence.
On Thursday, UEFA stressed a key role for players to help curb the problem, when it ratified a proposal on tackling discrimination presented by its Professional Football Strategy Council, which is chaired by President Michel Platini.
"We will have some very heavy sanctions against these people and so we are trying to set up a laws, rules and means so that we can address this issue and the national associations can also fight racism," Platini said.
Players and coaches, "namely those with most influence on the perpetrators of racist acts — (should) speak out, even if this may mean criticizing their own fans or players," UEFA said in a statement.
In another high-profile English Premier League case last season, Liverpool stood by Luis Suarez, who served an eight-match ban for racially insulting Man United defender Patrice Evra.
The debate on racism in European football intensified this season after incidents including a bad-tempered match between Serbia and England in an Under-21 European Championship playoff, and stadium closures imposed by FIFA on Hungary and Bulgaria for World Cup qualifiers.
AC Milan midfielder Kevin-Prince Boateng's decision to walk off the pitch, causing a friendly against a fourth-tier Italian club to be abandoned, led FIFA to appoint him to a task force studying the problem.
The UEFA strategy panel, which included delegates from national associations, leagues, clubs and players' unions, met on Wednesday in Sofia and urged competition organizers to tell referees "to stop matches in cases of racism."
Still, UEFA's claim of zero tolerance of racism comes after it declined to open disciplinary action against Zenit St. Petersburg after a Europa League match two weeks ago against Basel, where Russian fans reportedly targeted monkey noises at the Swiss club's players.
Basel midfielder Cabral, who is black, suggested the match was too finely poised, as his team defended a 2-1 aggregate lead with 10 men, to follow Boateng's example.
"Of course, the referee should have intervened," Cabral was reported telling Swiss media. "Maybe if we were going to be eliminated, I would have left the pitch, but there ..."
The UEFA statement on Thursday called on state authorities to "play their part."
"Providing the football bodies with the necessary legal means; acting and emphasizing to arrest, prosecute and ban from stadia for significant periods those responsible for racist acts; allowing the exchange of information regarding racist activities between states and football bodies," UEFA said.
The proposal stated UEFA's "full and unconditional opposition to any form of discrimination."
___ AP Sports Writer Graham Dunbar contributed to this report from Geneva.