Justin Welby told the BBC he had spent Christmases alone and had "no illusions about how dark it feels".
"But as the vaccine comes in, things will change," the archbishop said.
He urged people to take practical steps to avoid loneliness and plan for proper celebrations in the future.
He also said the elderly and vulnerable should not feel compelled to go to church this Christmas.
On Saturday, the planned relaxation of Covid rules for Christmas were scrapped for London and parts of south-east and east England and cut to just Christmas Day for the rest of England, Scotland and Wales.
Speaking on The Andrew Marr show, the archbishop acknowledged that for many families this year has been difficult and that many will be feeling lonely.
Asked directly whether Christmas was cancelled, he replied: "No. The celebrations are cancelled - we'll come to those again.
"This is very different to what we hoped for and longed for and it is the most intense pain for a lot of people.
"But it's not cancelled because at the heart of Christmas is Jesus coming into the world, God coming into the world and then coming onto Easter.
"This is a moment of God saying 'I am with you in the mess and there is hope'."
The archbishop said people should share memories of lost loved ones, speak to friends and family, and make plans for the future when the pandemic has eased.
He said: "Talk to people on the phone - ring, share and plan.
"Something about planning for the future helps us dream.
"What are you going to do? What are we going to do when this time is over?
"It may be many months yet but as the vaccine comes in things will change.
"What are we going to do to celebrate?
"And to mourn and to grieve, but crying and laughing to celebrate."
The Archbishop of Canterbury also said people needed to decide for themselves whether it was too risky to attend church at Christmas.
Places of worship will remain open over the festive period, even in areas in tier four - the toughest level of restrictions in England.
He said his mother, who is in her 90s, would not be going because it was "too dangerous".
"There are clergy who have underlying health conditions, who will not be going to church," he added.
For those who decide to attend church in person, they should not "mingle" after services and should stay away from the choir.
"Wave happily to people and go home," he said.