The Stoke City goalkeeper believes that fines are not enough of a deterrent for national associations and suggests points deductions or forfeits may be more effective
The Serbian Football Association came under the microscope last week after denying that England Under-21 international Danny Rose was racially abused during the Euro 2013 qualification playoff tie between the two countries.
Begovic believes that fines are not a sufficient deterrent for most nations and has called for forfeits and points deductions to be introduced.
"Financial punishments are not as big a deal to most countries, certainly to bigger FAs," Begovic told BBC Sport.
"Maybe teams should have to forfeit games or lose points - which means everyone suffers - so people learn."
Begovic, a Bosnia international, expressed his disappointment at the reaction of the Serbian FA to the accusations levelled at their supporters after Stuart Pearce's team's 1-0 victory in Krusevac.
The 25-year-old believes that the problem of racism is well-managed in England despite the recent high-profile suspensions handed out to Luis Suarez and John Terry.
"The comments from the Serbian FA are a huge shame," Begovic commented. "Hopefully the authorities will take the right actions to punish that kind of behaviour and the individuals will be disciplined.
"Here in England the situation is very good - there are not as many incidents as there may be in other countries but hopefully they can get rid of it all together.
"It is difficult to handle these situations because people in other countries may not be as educated about the racism issue as they are in this country and may not see it as such a foul thing as we do."