The Prime Minister said there will be "bumpy" months ahead, though he hopes the situation will be "radically different" by spring.
He said people should behave "fearlessly" but with common sense as the UK struggles to both contain the virus and keep the economy going.
In a BBC Andrew Marr Show interview to coincide with the Conservative Party conference, Mr Johnson:
* Admitted frustration with failings in the NHS Test and Trace programme.
* Blamed revellers who "hobnob" outside pubs for chaotic scenes in town and city centres following the 10pm curfew.
* Rejected Tory attacks on the limits imposed on people's freedoms as part of the effort to tackle the spread of Covid-19.
More than a third of people in the UK currently live under some form of extra restriction following an increase in coronavirus cases.
On the national stage, England's "rule of six" - which covers young children, unlike similar restrictions in Wales and Scotland - poses a major threat to many families' Christmas plans.
Mr Johnson said: "If you ask me 'do I think things can be significantly different by Christmas?' Yes I do, and we're working flat-out to achieve that.
"But be in no doubt that it is still very possible that there are bumpy, bumpy months ahead.
"This could be a very tough winter for all of us - we've got to face that fact."
Mr Johnson suggested the picture could be "radically different" by spring 2021.
The Prime Minister said new treatments are now available, adding: "We will find all sorts of ways, I'm absolutely sure, particularly through mass testing programmes, of changing the way that we tackle this virus."
But he acknowledged the existing NHS Test and Trace service, run by Tory peer Baroness Harding, is not perfect.
Just 38.1% of people tested for Covid-19 in England in the week ending September 23 at a regional site, local site or mobile testing unit - a so-called "in-person" test - received their result within the 24-hour target set by the Prime Minister.
He conceded: "It is not perfect, I'm not going to claim it's perfect. Am I frustrated with it? Yes, of course I'm frustrated with it."
But he stressed he does not blame NHS Test and Trace, adding: "I take full responsibility for the service, by international comparators it is really very, very good indeed."
The Prime Minister acknowledged that people were "furious" with him and his Government over the handling of the pandemic.
Mr Johnson has previously accused members of the public of being "blase" and "complacent" over the threat posed by the virus.
He said: "I appreciate the fatigue that people are experiencing... but we have to work together, follow the guidance and get the virus down whilst keeping the economy moving."
Mr Johnson defended the 10pm curfew, which has seen crowded scenes as drinkers and diners leave bars and restaurants at the same time.
"Obviously it makes no sense if, having followed the guidance for all the time in the pub they then pour out into the street and hobnob in such a way as to spread the virus."
Measures such as the curfew have fuelled Tory resentment from influential MPs including Steve Baker and 1922 Committee chairman Sir Graham Brady about restrictions which have caused widespread economic damage.
Mr Johnson said: "I'm a freedom-loving Tory. I don't want to have to impose measures like this, are you crazy?
"This is the last thing we want to do. But I also have to save life. And that's our priority."
Meanwhile Labour stepped up demands for Mr Johnson to explain the way local measures are imposed, suggesting there could be "political interference" meaning Tory areas were spared the toughest restrictions.
"Because there is no clear guidelines as to why an area goes into restrictions and how an area comes out of restrictions then there is a suspicion that there is political interference - I hope there isn't," he said.
"But until the Government publish clear guidelines, that suspicion will always linger."