"Football is an inclusive sport, open to everyone," he said. "Unfortunately, some people have still not grasped this concept, which is why we're going to have to rethink our approach.
"We need to target offenders more effectively when a player is subjected to racist, homophobic or sexist insults during UEFA competitions. We’re here to protect the players."
Ceferin was addressing the Ordinary Congress of European soccer's governing body in Lisbon, where he was later was re-elected as UEFA president unopposed.
Liverpool on Tuesday called for an end to "vile chants" about the Hillsborough Stadium disaster after they were heard during the 0-0 Premier League draw with Chelsea at Stamford Bridge.
The 1989 FA Cup semi-final was the scene of Britain's worst sporting disaster when 97 Liverpool fans lost their lives after a crush in an over-crowded and fenced-in enclosure.
Chelsea apologised and said "hateful chanting has no place in football".
The Premier League said it condemned the "tragedy chanting" at the match.
Inter Milan striker Romelu Lukaku - who is on loan from Chelsea - was racially abused by Juventus fans during their Italian Cup match, also on Tuesday, the BBC reported.