The Labour leader said his party “didn’t succeed in delivering the change that so many people so desperately need” after suffering its worst general election result in 85 years.
He said his Labour should use the Christmas period to “listen, reflect and remember all the things that bind us together”.
Meanwhile Boris Johnson used his message to promise help for persecuted Christians across the world.
Mr Corbyn is expected to step down early in 2020 after overseeing a leadership contest to elect his successor.
In his last Christmas message as Labour leader, he said: ”This has been a difficult year for many of us. We didn’t succeed in delivering the change that so many people so desperately need. But Christmas is a chance to listen, reflect and remember all the things that bind us together: our compassion, our determination to tackle injustice and our hope for a better world.
“At Christmas too often the scale of injustice and inequality is in very plain sight. As people hurry home through our busy high streets, often loaded with shopping bags, seeing those who have no homes and no hope beside them. Adverts for mouth-watering Christmas meals, when we know that many children are hungry. And while we celebrate being together, we are reminded of the many who will be alone and sadly lonely at Christmas.
Thanking those who will be working over Christmas, he added: “This Christmas I know so many people will be out supporting those who are less fortunate: helping in food banks, working in shelters and trying to find children who are homeless emergency shelter; and our brilliant National Health Service workers and all those who work in our public services, who will keep us safe over Christmas.
“Together we have the power to bring about change in our communities and make a real difference to the lives of others. Together, let’s do all we can to make this a country that cares for the many and not the few.”
Mr Johnson also thanked NHS workers and members of the armed forces, and vowed to tackle the persecution of Christians across the world.
However, his reference to people spending Christmas in prison cells is likely to draw attention to the plight of Nazanin Zaghari-Raticlife, the British citizen jailed in Iran after being accused of working for the British government.
Mr Johnson, then the foreign secretary, drew heavy criticism in 2017 after wrongly telling a parliamentary committee that the mother-of-one had been training journalists in Iran – a suggestion leapt on by the Iranian regime as further justification for keeping her behind bars.
In his Christmas message, the prime minister said: “On behalf of the whole country I want to say a huge thank you to our amazing NHS staff, many of whom will be working throughout the holidays to take care of us. Thank you also to our police, and all those public servants working tirelessly this Christmas.
“I also want to express my personal gratitude to the wonderful members of our armed forces currently on deployment – and therefore to their friends, family and children back home who will have an empty chair at the table when they tuck in to their Christmas dinner.”
He added: “Today of all days, I want us to remember those Christians around the world who are facing persecution. For them, Christmas Day will be marked in private, in secret, perhaps even in a prison cell.
“As prime minister, that’s something I want to change. We stand with Christians everywhere, in solidarity, and will defend your right to practice your faith.”