The Christian message of "peace on earth and goodwill to all" is "needed as much as ever", the Queen has said in her Christmas Day broadcast.
She said the message is "never out of date" and can be "heeded by everyone".
The Queen also joked that family events during a "busy year", including weddings and births, had kept "a grandmother well occupied".
The monarch, 92, highlighted the importance of people with opposing views treating each other with respect.
It comes as Parliament remains divided over the PM's Brexit deal, as the UK prepares to leave the EU in March.
However, as head of state, the Queen is publicly neutral on political matters.
In the broadcast, recorded in Buckingham Palace's white drawing room, the Queen referred to 2018 being a "year of centenaries" , recalling how her father served in the Royal Navy during World War One and "like others, he lost friends in the war".
"At Christmas, we become keenly aware of loved ones who have died, whatever the circumstances," she added.
The message, which was recorded on 12 December, includes highlights of 2018, from the Commonwealth Games and England reaching the World Cup semi-finals to the weddings of the Duke and Duchess of Sussex and Princess Eugenie and Jack Brooksbank, and the 70th birthday of the Prince of Wales.
And she looks ahead to the birth of first child of the Duke and Duchess of Sussex next spring.
The Queen added: "Some cultures believe a long life brings wisdom. I'd like to think so.
"Perhaps part of that wisdom is to recognise some of life's baffling paradoxes, such as the way human beings have a huge propensity for good, and yet a capacity for evil."
She went on to talk about the summit of Commonwealth leaders at Windsor in April, saying the Commonwealth's "strength lies in the bonds of affection it promotes, and a common desire to live in a better, more peaceful world.
"Even with the most deeply held differences, treating the other person with respect and as a fellow human being is always a good first step towards greater understanding."
She emphasised her own strong Christian beliefs in the broadcast.
She said: "Through the many changes I have seen over the years, faith, family and friendship have been not only a constant for me but a source of personal comfort and reassurance."
By BBC royal correspondent Nicholas Witchell
Were the Queen's words in her Christmas broadcast an oblique, coded encouragement to the different sides in the Brexit debate to treat each other with greater respect?
It really isn't clear. When she talked about "deeply held differences" she was actually talking about the unifying power of the Commonwealth.
When she referred to the need for "peace and goodwill" she was referring to the story of the birth of Jesus.
She never mentioned the word "Brexit" at all.
It wouldn't have been difficult to have fashioned a speech which referred to the intense political debate in the UK and which urged people to keep in mind that there is "much more that unites us than those things that divide us".
But Elizabeth II is an extremely cautious monarch, wary of saying anything which might be deemed politically contentious. It is a principle which has been exercised with some skill and which has served her throughout her long reign.
Some might say that this was one moment when Britain's head of state might have used her immense authority to try to calm the Brexit debate and reassure the country that we can cope, whatever the outcome.
She and her advisers chose not to be explicit.
But notwithstanding the lack of clarity in the speech itself, it is clear that the Palace - by highlighting the passages about goodwill and treating each other with respect - is hoping that the wider world will interpret the broadcast as an attempt by the monarch to soothe the whole Brexit debate.
The Queen wore an Angela Kelly ivory silk cocktail dress, with a gold Scarab brooch, with ruby and diamond embellishments, for the broadcast produced this year by Sky News.
The brooch was a 1966 gift from the Duke of Edinburgh.
She was sitting beside a framed black and white photograph of herself, Prince Philip and a baby Prince Charles, taken in 1948.