She said he was born and brought up in Liverpool and later lived and worked in London before moving to live in Israel with his family.
“He was a peaceful man, not politically involved. He only wanted peace,” she said.
Ms Hirschfield described her concern after reports began to emerge of the attack, which happened in Jerusalem’s Har Nof neighbourhood, an ultra-Orthodox area.
She told the BBC: “I heard the news this morning so texted my cousin to check he was OK. When I heard nothing back, I called my sister who lives nearby.
“She tried calling him too but when she got no reply she went to the house. [Mr Goldberg’s] son was there – very distressed. He said his mum had gone to the synagogue to get more information.
“After a while, my sister called me to say that he had indeed been killed.”
It is thought Mr Goldberg moved to Israel from Golders Green, north London, in the early 1990s. He held dual British-Israeli citizenship.
Israeli police confirmed the other three dead victims were Americans who also held dual citizenship. They were named as Mosheh Twersky, Aryeh Kupinsky and Cary William Levine.
Thousands of people attended funerals of the victims in Jerusalem.
The attack early today prompted condemnation from British politicians.
Prime Minister David Cameron said: “I’m appalled by today’s horrific attack on worshippers at a Jerusalem synagogue. My thoughts are with the victims’ families.”
Labour leader Ed Miliband wrote on Twitter: ” My thoughts are with the families of the victims and people of the holy city. I’m horrified by the barbaric attack on the synagogue in Jerusalem – an appalling act of terrorism to be totally condemned.”
Earlier Foreign Secretary Philip Hammond joined US secretary of state John Kerry in condemning the attack. Speaking in London, Mr Kerry and Mr Hammond called on the Palestinian leadership “at every single level” to condemn the assault.
“To have this kind of act, which is a pure result of incitement, of calls for days of rage, of irresponsibility is unacceptable,” Mr Kerry told reporters.
© Provided by Press Association An ultra-Orthodox Jewish man prays at the scene of the attack in Jerusalem (AP)”The Palestinian leadership must condemn this and they must begin to take serious steps to restrain any kind of incitement that comes from their language, from other people’s language, and exhibit the kind of leadership that is necessary to put this region on a different path.”
Mr Hammond added: “Both sides in this conflict need to do everything possible to de-escalate the situation and reduce the tension we’ve seen in Jerusalem over the past few weeks, which is extremely dangerous for both Palestinian and Jewish communities in that area.”
The attack comes amid heightened tensions in the city, with a wave of attacks by Palestinians on Israelis killing at least six people in recent weeks.
Israeli prime minister Benjamin Netanyahu denounced the violence as the “cruel murder of Jews who came to pray and were killed by despicable murderers”.
He blamed the attack on incitement by the Islamic militant group Hamas and Palestinian president Mahmoud Abbas, which he said the international community had been “irresponsibly ignoring”.
A Foreign Office spokesman said: “We are aware of the death of a dual British-Israeli national in Israel on November 18, 2014.”