The British government should have done more to free Alan Henning, the murdered hostage's brother-in-law has said.
Colin Livesey described Mr Henning's killers as "scum" and said the family had lost a "great person".
A video purporting to show the 47 year old being beheaded has been released by Islamic State (IS) militants.
Prime Minister David Cameron described the murder as "completely unforgivable" and vowed the UK would do all it could to find those responsible.
Salford taxi driver Mr Henning was delivering aid to Syria in December when he was kidnapped.
Speaking to the BBC, his wife Barbara's brother Mr Livesey, said: "My heart's just sunk to a level that I never thought it could do.
"I'm just devastated for my sister and two kids for what they've gone through, and it's so hard.
"We're all just saddened knowing that we've lost a great person in our family."
Regarding Mr Henning's killers, Mr Livesey said: "I just hope and pray they get what's coming to them.
"I've just so much hatred for them."
But he added the government could have done more for Mr Henning in captivity, "when they knew about it, months and months ago".
The prime minister described Mr Henning as a "kind, gentle, compassionate and caring man".
Speaking at Chequers following a briefing from defence and intelligence officials, including the head of MI5, Mr Cameron said the murder was "absolutely abhorrent".
"It is senseless, it is completely unforgiveable," he added.
"Anyone in any doubt about this organisation can now see how truly repulsive and barbaric it is.
"And as a country, what we must do, with our allies, is everything we can to defeat this organisation in the region, but also to defeat it at home, and we must do everything we can to hunt down and find the people who are responsible for this."
Alan Henning was on his fourth aid mission to Syria
IS had threatened to kill Mr Henning in video footage last month showing the death of Briton David Haines.
In the most recent video, the extremist group threatens US aid worker Peter Kassig.
BBC security correspondent Gordon Corera said the footage was similar to previous videos released by IS and included a reference to last week's vote by Parliament to authorise air strikes against IS in Iraq.
Like previous videos it features a militant who, from his accent, appears to be from Britain.
Mr Cameron said "all the assets" the government has would be used to try to find and help remaining hostages.
He added the government would "do everything we can to defeat this organisation which is utterly ruthless, senseless and barbaric in the way it treats people".
'Man of great peace'
Volunteer Mr Henning, 47, was on his fourth aid mission to Syria when he was captured within minutes of arriving in the country last December.
The prime minister said: "Alan Henning was a man of great peace, kindness and gentleness.
"He went with many Muslim friends out to do no more than simply help other people.
"His Muslim friends will be mourning him at this special time of Eid and the whole country is mourning with them."
The prime minister met ministers and officials at Chequers on Saturday
Mr Henning's wife had this week appealed for her husband's release, saying: "He is innocent."
She asked for "mercy", saying the family was still trying to communicate with her husband's captors. Mr Henning's family had earlier received an audio message of him pleading for his life.
Deputy Prime Minister Nick Clegg said Mr Henning was trying to help Muslims and had been "brutally murdered by an organisation that's twisting that religion to its own end".
His message to IS, also known as Isil or Isis, was: "If you are doing this to intimidate us, you won't. If you are doing this to break our resolve, you won't.
"If you are doing this to drag us into a religious war on your terms, you won't.
"What we in Britain will do instead in a calm and determined way is to play our role to hunt you down and to rid the world of this barbaric violence."
Frank Gardner, security correspondent
David Cameron's vow to catch the jihadist killers of Alan Henning and bring them to justice would seem to match the mood of the nation.
But judging by the track record of previous such cases of hostages being murdered overseas, this promise has little likelihood of being fulfilled.
Tony Blair made the same pledge after Ken Bigley from Liverpool was beheaded in 2004, Gordon Brown did the same when tourist Edwin Dwyer was kidnapped and killed in the Sahara, and Mr Cameron vowed to punish those who besieged the Algerian gas plant last year.
According to the Crown Prosecution Service, there has not been one single case of any murderers of British hostages ever being brought to justice in Britain.
IS has previously released videos showing the apparent beheading of two US journalists, James Foley and Steven Sotloff, and British aid worker Mr Haines.
The video released on Friday is yet to be verified, but it appears to show Mr Henning kneeling beside a militant dressed in black, in a desert setting.
The footage ends with an IS fighter threatening a man they identify as Mr Kassig.
In a statement, Mr Kassig's family said he had converted to Islam. They referred to him as Abdul Rahman Kassig.
The family asked people to pray that he and "all innocent people being held hostage in the Middle East and around the globe" would be freed.
They also asked people to pray for Mr Henning's family, adding: "We have read about his work and his generous character with great respect and admiration."
John Cantlie was kidnapped in Syria in 2012
Earlier on Friday, the father of another hostage, British journalist John Cantlie, appealed for him to be released "to those he loves and who love him".
The journalist, who was kidnapped in Syria in 2012, has so far appeared in three videos in which he has delivered scripted messages responding to military attacks on IS.
RAF Tornados first hit IS targets on Tuesday, four days after Parliament authorised UK involvement in an international military campaign.
The aircraft have been conducting daily flights over Iraq, and carrying out air strikes against vehicles and weapons positions to assist Kurdish and Iraqi army ground forces.
IS has seized large parts of Iraq and Syria and declared a so-called caliphate in the areas it has taken.