Webb's quick reaction when Fabrice Muamba collapsed on the field in March helped the Bolton midfielder get treatment which saved his life.
Referees' responses could be affected if players "cry wolf" too often, Webb said on Thursday.
Players who are not seriously injured sometimes seek a tactical edge by staying down longer than necessary to slow the game.
"I would ask everybody in football to think about these situations and ask players not to take advantage," the English referee said.
Livorno midfielder Piermario Morosini died after suffering cardiac arrest during Italy's Serie B match in April.
Muamba's recovery after his heart stopped beating on its own for 78 minutes is "an unbelievable miracle," Webb said.
FIFA invited Webb to address a two-day gathering of medical professionals, who have received a comprehensive study of cardiac cases involving football players from the game's governing body.
FIFA's registry includes 84 players, who died after cardiac arrest in the past five years, and 23 cases of players, who - like Muamba - survived. Five sudden deaths remain unexplained.
FIFA President Sepp Blatter said more needs to be done to protect players' health.
"We have to send practically every week a letter of condolences to one of the national associations because somebody died," Blatter told delegates.
Research from 123 countries revealed the average age in cases that have resulted in death was 24.9 years. The youngest player affected was 13, according to FIFA's chief medical officer Jiri Dvorak.
Dvorak told delegates that only half of the countries surveyed required players at top-tier clubs to undergo echocardiograph tests. Heart screenings are mandatory for all players at FIFA tournaments.
Delegates raised concern over the fact that defibrillators - which are used to restart the beating of a player's heart with an electric shock - had been available only in 23 emergency cases. They cost from $600-$1,200.
FIFA delegates learnt that players will die without receiving an electric shock within three minutes of collapsing.
Webb said referees are under pressure when deciding on stopping the game and have a fallen player receive treatment. He warned players against faking pain for fear of affecting referees' judgment.
"If players and if people cry wolf too many times, then there is a possibility that maybe we will not react in the way we need to," Webb said on the sidelines of the meeting. "If we come under criticism for stopping the games too many times for doctors or physiotherapists to enter the field of play, then referees might be inclined not to stop the game."
Players' welfare is first priority, Webb said, adding that he felt a "numb sensation" after Muamba collapsed during an English FA Cup match at Tottenham.
"Without life, there is no football at all. The realization is, when the CPR starts, is just how serious it is," he said. "This story has a happy ending thanks to the expertise of the medical staff."
The crowd at White Hart Lane was "urging the doctors to get (Muamba) going again," Webb said. "It was just the most unbelievable crowd reaction I have ever experienced in football and thinking about it now is making me feel emotional."
Muamba was discharged from a London hospital on April 16, but cardiologists have not decided when he can resume playing.
Also discussed at the conference was a possibility that referees — like players — could be asked to undergo tests for banned performance enhancing drugs.
Referees are part of the game and should be treated like players, Dvorak said.
Meanwhile, the World Anti-Doping Agency asked FIFA to advise when players serving doping bans should be allowed to return to training with teammates.
Current rules under review prevent suspended players working with their teams — effectively extending their ban if they are not match-ready immediately on completion.
WADA director general David Howman acknowledged that penalties could seem harsher for team players than for individual athletes.
FIFA and WADA are also working on a biological passport to monitor players' doping samples ahead of the 2014 World Cup.
Delegates agreed that players should ideally play a maximum of 60 games each year to protect themselves against injury and issues such as osteoarthritis.