The comments were made on Starcom Network's Voices And Views last Sunday.
Sylvester Forde and Dr Kim Norville, relatives of the late Cheryl Hinds, complained on the radio programme that Hinds died six hours after arriving at the hospital without receiving what they claimed was timely medical care and attention.
An upset Forde told moderator David Ellis that in relation to the question on capital punishment in Barbados, he had told some people that "there is no need for bringing a gallows to Barbados. What you do is send somebody to the QEH there they will die".
His niece Norville, a medical doctor in Connecticut in the United States, said her grandfather died at the hospital from bed sores following a successful surgery. She added that for someone to die from bed sores indicated a serious breach in nursing care.
Yesterday, while leading the debate in the House of Assembly on the Queen Elizabeth Hospital (Amendment) Bill, Walcott said while he understood the family's hurt, he was not pleased with some of the comments made.
"It is unfortunate. I understand their sentiments. I understand the hurt of the relatives. But when on the airwaves you can have a person say that you don't need a gallows, you can just send people to the hospital and they will die, what is that, Sir? And that is broadcast throughout Barbados and the Caribbean and on the Internet."
He added that in the United States "that we hold up as a beacon of everything", 195 000 people died every year and over the past three years over 600 000 people had died due to medical negligence, mistakes and malpractice.
"In that programme we heard from a physician that we are concerned in this country about open heart surgery and dialysis and not concerned about the basics and bed sores . . . . Throughout the world people get bed sores. In 2003 we had 139 bed sores at the QEH; 49 of these persons were admitted from at home with sores. In 2004 there were 154 and 40-something were admitted form home.
"But when we compare, the US had over 511 000 bed sores. What are they concerned about? And you are coming from there to try to tell us that we are neglecting an area?" Walcott asked.