Jennah Bawa, eight, had been on a shopping trip with her Kenyan-born mother, Zahira, on Saturday.
Businessman Louis Bawa, of Leamington Spa, Warwickshire, said he had spoken to them on Friday but "didn't get a chance to catch up with them" again.
"This time they didn't come home."
The official death toll stands at 62, with more than 170 injured.
The UK government says five of the dead people have been confirmed as British, with another one thought to be British.
Meanwhile, the Foreign Office said it was aware of comments by Kenya's foreign minister that a British woman was among foreign nationals involved in the attack.
Amina Mohamed said the Briton was a woman who has "done this many times before" and two or three Americans were also among the suspected militants.
A Foreign Office spokeswoman said: "We continue to liaise very closely with the Kenyan authorities and to support their investigation into this attack."
Kenyan security forces say they have now taken control of all floors of the shopping centre in Nairobi, although an explosion and gunfire was heard from there on Tuesday morning.
The Somali Islamist movement al-Shabab says it carried out the attack at the Westgate shopping mall in retaliation for Kenyan military operations in Somalia.
In an interview with the Daily Telegraph, Mr Bawa, 43, said his wife and daughter were both Muslims but were killed by "animals" who were using "religion as an excuse to kill people... They're saying that they were targeting certain people, but they were targeting anyone".
The family lived in Leamington Spa until last year, when lawyer Mrs Bawa is reported to have returned to Kenya to look after her mother. Mr Bawa then took a job as the chief executive of a marketing company in Dubai and began commuting to his family in Nairobi at weekends.
He told the paper: "The last time I spoke to them was on Friday evening, I didn't get a chance to catch up with them on Saturday morning. They were going to Westgate to do what they always did, grocery shopping. This time they didn't come home.
"I think our last conversation was about just normal things, school fees, something like that, I can't remember. I don't know exactly what happened but it looks to me that they were gunned down ... they were just shot."
Mr Bawa began waiting outside the mall on Sunday for news of his family.
Describing the moment he realised they were among the victims, Mr Bawa said: "At first I was convinced that they would be OK. I had hope. Then on Sunday night there was a team that went in to bring out some bodies and they took photographs of other bodies.
"We all had to look at these pictures - something I would never want anyone to have to do - and identify them. That was how I knew. My heart just stopped, that was the last news in the world I wanted to hear. It's like nothing else, I can't fathom it, even now."
He added that last week he had promised Jennah that he would buy her any "present in the world" if she did well in her exams.
Mr Bawa said: "She said she wanted a pony, a particular coloured pony but she said she thought even though her exams were not until December, she better tell me now so I could start saving up because she was going to work very hard."
Architect Ross Langdon, who had British-Australian citizenship, has also been named as one of the UK victims although the Foreign Office is still not confirming identities.
Mr Langdon's company, Regional Associates, issued a tribute to him and said he had died alongside his pregnant partner, Elif Yavuz, a Dutch citizen.
Another of those killed was a Peruvian public health consultant who had been set to take up a full-time post at Liverpool School of Tropical Medicine.
Dr Juan Jesus Ortiz-Iruri, 63, was due to arrive at its Centre for Maternal and Newborn Health this week.
After a meeting of the government's emergency committee Cobra on Monday, Defence Secretary Philip Hammond said the UK had been in contact with the Kenyan authorities throughout and with its own diplomatic representation in Nairobi.
Meanwhile, speaking at the United Nations in New York,  Foreign Secretary William Hague said the attacks were "not going to deter us or the people of Kenya from our continuing work in Somalia".
Al-Shabab, which is part of the al-Qaeda network, has repeatedly threatened attacks on Kenyan soil if Nairobi did not pull its troops out of Somalia.
There are about 4,000 Kenyan troops in the south of Somalia, where they have been fighting the militants since 2011.
British nationals concerned about friends or family can contact the Foreign Office on +44 (0)20 7008 0000.
A British man, whose wife and daughter died in the Kenyan shopping centre attack, has recalled the last time he spoke to them and the "heart-stopping" moment when he found out they had died.