The taunts were sung by some home fans during the second half of the 1-1 Premier League draw at Kenilworth Road.
Former Reds defender Jamie Carragher also condemned the chants, saying: “We’re better than that.”
Liverpool manager Klopp has previously spoken out against so-called ‘tragedy chanting’ between rival supporters and in July the Football Association issued a new charter outlining rules for dealing with the problem.
It followed the arrest of a Manchester United supporter at last season’s FA Cup final for wearing a shirt that mocked the victims of Hillsborough.
After the Luton match, Klopp said he did not hear the chanting, which occurred while the game was still goalless shortly after half-time, but added: “Shame on everyone who said it.”
Speaking on Sky Sports, Carragher said: “At the start of the season I was involved in something with supporters coming together about tragedy chanting.
But the world we live in right now, I think we’re better than that— Jamie Carragher
“I’ve just heard that a couple of times in this game. As supporters you’ve got to have rivalry, there is no doubt. But we’re better than that.
“It’s happened two or three times in the game. All clubs have been guilty of that over the years at different times.
“But the world we live in right now, I think we’re better than that.”
Liverpool earned a dramatic point five minutes into added time when substitute Luis Diaz cancelled out Tahith Chong’s 80th-minute goal for Luton.