Mr Constance was scathing in his assessment of the prime minister's response to bushfires blazing across Australia.
"I haven't had a call from him so to be honest with you the locals probably gave him the welcome he deserved," the Liberal MP, who fought to save his home at Malua Bay from the New Year's Eve bushfires, said.
"I'd say this to the prime minister today: the nation wants you to open up the cheque books.
"I know this is tough and I know I'm on his side of politics. But the only two people who are providing leadership at this stage are (NSW Rural Fire Service commissioner) Shane Fitzsimmons and (NSW premier) Gladys Berejiklian."
One Cobargo resident called Mr Morrison an idiot, while someone else shouted that he would be getting no votes from the community.
When one woman did not immediately take the prime minister's outstretched hand, he reached down to grab her hand to shake it.
"I'm only shaking your hand if you give more money to the RFS, so many people here have lost their homes. We need more help," she said during the Thursday visit, before Mr Morrison patted her on the back and walked away.
'I don't take these things personally'
As footage of the angry reaction to his visit made headlines around the world, Mr Morrison told Melbourne radio station 3AW that he did not take verbal abuse personally.
“I know people are angry and they’ll often fixate on … a prime minister or someone else,” he told 3AW’s Neil Mitchell.
“I understand that. I understand the emotion, I understand the hurt, the anger and frustration.
“All I know is that they’re hurting and it’s my job to be there to try and offer some comfort and support.
“I don’t take these things personally. Why would I?”
Mr Constance called on Mr Morrison to immediately provide money for victims to buy supplies.
"We've lost a lot of homes. A lot of businesses. I know people who have lost both," he said.
"Having lived through this myself, it's tough. You can't experience this, it's cruel, it's nasty.
"The feeling is bloody raw and it's bloody raw for a reason. I was here at Malua Bay the other day and it's just hell on earth."
Later on Thursday, Mr Morrison was also snubbed by a firefighter who had lost his home in the blazes.
"I don't really want to shake your hand," he told Mr Morrison, before walking away.
Afterwards, the prime minister asked the incident controller to "tell that fella, I'm really sorry, I'm sure he's just tired."
The incident controller responds: "No, no, he lost a house."
The prime minister received a much warmer welcome when he arrived at the Lucknow Memorial Hall in East Gippsland where they have been collecting goods since New Year's Eve.
Lynn Wallwork, who lost her home in the fires at Sarsfield, said she was glad to see Mr Morrison at the centre.
"It's a tough road ahead," Mr Morrison said to her.
Federal natural disasters minister David Littleproud on Thursday announced disaster relief payments would be extended to bushfires survivors in the Bega Valley.
Payments of $1000 per adult and $400 per child can be claimed through the Department of Human Services.
"This is for people whose home has been severely damaged or destroyed, who've been seriously injured or who've lost a family member," the minister said.