The family was torched around 10.30 pm at Glencaw Park in the Galliagh area of the city.
They said: “We are truly overwhelmed by the support we have received from our family, from across this city and across the island.
“The support we have received from SDLP members and the party’s leadership has been incredible and we’d like to thank them for that.
“The kind words, too, from across the political spectrum, including the Secretary of State has been a source of comfort to us both.
“We will not be deterred by this attack and it will not stop the work that we’re engaged in to make Derry a better place for everyone living here.
“The generosity that we have seen, from across the city and from across the island, far outweighs the hate of those who carried out this act.
“We are Derry people. We are proud to have the support of the people of Derry. And we’ll continue to do all we can to make this city a better place.”