Thousands of "small acts of goodness" can make a difference, even though the world's problems often seem too big to change, the Queen has said.
In her annual Christmas Day address she said she drew strength from "ordinary people doing extraordinary things".
After paying tribute to the UK's Olympians and Paralympians, she spoke of her admiration for "unsung heroes".
She spoke about being inspired by the dedication of volunteers, carers, community workers and good neighbours.
Meanwhile, the Queen did not attend church on Christmas Day, with Buckingham Palace saying she was still suffering from a heavy cold.
A spokesman said she was staying indoors at Sandringham, her Norfolk estate, to help her recover, but added that she would still participate in the family's Christmas Day celebrations.
Prince Philip, Prince Charles, Prince Harry and other royals did attend church at Sandringham, while the Duke and Duchess of Cambridge went to church in Berkshire, where they are spending Christmas with the Middleton family.
In her 10-minute Christmas message, filmed in Buckingham Palace's regency room, the Queen spoke about the theme of inspiration, talking about the achievements of Olympians and Paralympians at Rio 2016
"Having discovered abilities they scarcely knew they had, these athletes are now inspiring others," she said.
Her Majesty said she had been inspired by the "dedication" of doctors, paramedics and crew at the East Anglian Air Ambulance, where the Duke of Cambridge works as a helicopter pilot.
The Queen opened the service's new base in July.
However, she said inspirational people "don't have to save lives or win medals".
"I often draw strength from meeting ordinary people doing extraordinary things: volunteers, carers, community organisers and good neighbours; unsung heroes whose quiet dedication makes them special," she said.
The Queen said problems around the world - including wars and injustice - often seem too big to change.
"When people face a challenge they sometimes talk about taking a deep breath to find courage or strength. In fact, the word 'inspire' literally means 'to breathe in', she said.
"But even with the inspiration of others, it's understandable that we sometimes think the world's problems are so big that we can do little to help.
"On our own, we cannot end wars or wipe out injustice, but the cumulative impact of thousands of small acts of goodness can be bigger than we imagine."
She said the 600 charities of which she is patron - many of which joined the Queen for a 90th birthday lunch in The Mall this summer - "inspire me with the work they do".
"From giving friendship and support to our veterans, the elderly or the bereaved, to championing music and dance, providing animal welfare, or protecting our fields and forests, their selfless devotion and generosity of spirit is an example to us all," she added.
Earlier this week, Buckingham Palace said the Queen would step down as patron of 25 charities and organisations, including the NSPCC, Battersea Dog's Home and Save the Children.
Her Majesty also reflected on the achievements of the Duke of Edinburgh's Award, which celebrated its 60th anniversary this year, and The Prince's Trust, which was 40 years old in 2016.
"These started as small initiatives but have grown beyond any expectations and continue to transform young people's lives," she said.
She added: "The message of Christmas reminds us that inspiration is a gift to be given as well as received and that love begins small but always grows."
For the occasion, the Queen wore a deep jade, silk cloque dress by Angela Kelly, as well as a pearl and diamond brooch previously worn by the late Queen Mother.
The televised address, which was also broadcast across the Commonwealth, was recorded before news broke that her granddaughter, Zara Tindall, had lost her baby.