In a televised message broadcast at 8pm on Sunday evening, the Queen also recognised the pain felt by many families living through this "time of disruption".
She personally thanked front-line NHS staff, care workers and others carrying out essential roles for their efforts, in a personal message reflecting her experience in other difficult times, adding: “I’m sure the nation will join me in assuring you that what you do is appreciated and every hour of hard work brings us closer to a return to more normal times.
“I aso want to thank those of you staying at home, thereby helping to protect the vunerable and sparing many families the pain already felt by those who have lost loved ones.”
It comes as the UK death toll from the virus neared 5,000 after a rise of 621 coronavirus-related hospital deaths in the past 24 hours. In Scotland, there were another two reported deaths linked to Covid-19.
The Queen said in her address to the country and Commonwealth: "I hope in the years to come everyone will be able to take pride in how they responded to this challenge.
"And those who come after us will say that the Britons of this generation were as strong as any.
"That the attributes of self-discipline, of quiet, good-humoured resolve and of fellow feeling still characterise this country."
‘Grief’ and ‘financial difficulties’
She acknowledged the "grief" some have experienced, the "financial difficulties" many face, and the "enormous changes" the country is enduring, after almost two weeks of lockdown to tackle the spread of Covid-19.
With hundreds of thousands answering the call for NHS volunteers and others supporting vulnerable people in their communities, the monarch said she hopes in the future everyone will be able to feel "pride" in how they rose to the challenge.
Commenting on the difficulties facing the nation, the Queen, 93, said: "I am speaking to you at what I know is an increasingly challenging time.
"A time of disruption in the life of our country: a disruption that has brought grief to some, financial difficulties to many, and enormous changes to the daily lives of us all."
The Queen stressed that the coronavirus pandemic is a challenging time for us all but that, using the great advances of science, “we will succeed” and that this success would “belong to us all.”
She added: “Better days will return. We will be with our friends again, we will be with our families again, we will meet again.”
The televised address will be a rare event, with the head of state only making three previous appearances during troubled times.
Speeches were broadcast after the Queen Mother's death in 2002, ahead of Diana, Princess of Wales's funeral in 1997, and about the first Gulf War in 1991.
It was recorded at Windsor Castle under special circumstances after specific advice from the Medical Household was sought, and followed, to mitigate any risk to the Queen and others.
The castle's White Drawing Room was specifically chosen so an appropriate distance could be maintained between the Queen and the other occupant - a cameraman wearing personal protective equipment.
The Queen has been staying at her Berkshire home of Windsor Castle with the Duke of Edinburgh since March 19, arriving earlier than normal for the Easter period as a precaution amid the pandemic.