Mr Drakeford said he expected the Welsh government would extend the lockdown by another three weeks when it meets on Friday next week, although there might be scope to ease a few minor restrictions.
He said the number of coronavirus cases had fallen since the start of the latest lockdown. But he said the infection rate was still too high, and it was likely most of the measures would be retained for the foreseeable future.
But Mr Drakeford said he hoped that at least some of the rules could be lifted when the lockdown was reviewed again on February 18.
"If you go back to the middle of December, the infection rate was then 650 people per 100,000, and still going up, and in one or two local authorities there were over 1,000 cases per 100,000," he said.
"Now we're down to 270, and as a proportion of the population it's now going down."
But Mr Drakeford said that while the number of positive tests was falling, this had not yet resulted in a corresponding fall in hospital admissions.
"We will review the restrictions next Friday, so we will be looking at the evidence in the middle of next week," he said.
"But unless there is some startling new evidence, I can't see there being any significant relaxation of the rules.
"It might be that there are some very marginal changes we can make, but that is all it will be.
"However, when we look at it again in another three weeks, I would hope by that time there is more we can do."
He said the first priorities would be looking to make it easier for people to meet outdoors, where the risks were much lower.
Any reopening of schools was likely to be done on a phased basis, with different age groups going back at different times.
He said he did not wish to discourage people from planning Easter holidays in Wales, but advised them to check the cancellation policies when booking ahead.
Mr Drakeford said it had been a difficult time since the first lockdown was announced in March, but said there were signs that things would get easier in the coming months.
"We have now got the vaccination, something we didn't have in December, now we have got two, and there will be a third with us soon, that will make a massive difference over the coming months," he said.
He said improved testing meant that people who would previously have been forced to self isolate can now return to work.
Mr Drakeford added that as the weather improved, it would be possible to look at reintroducing more outdoor activities where the risk of transmission is less.
He said the pandemic had been a difficult time for everyone concerned, and could understand why there had sometimes been public anger about the measures being introduced.
"It's very hard when you do things ahead of others, but I find that the anger usually goes away quite quickly," said Mr Drakeford.
"When I decided to prohibit the sale of alcohol in restaurants and pubs before Christmas, there was a lot of opposition at the time, but it wasn't more than a week before people began to see why that was absolutely necessary," he said.
Mr Drakeford said there was no truth in claims that urban areas were being given priority when it came to distributing the vaccine. He said there had been no problem getting the vaccine into rural areas.
"The Welsh government's top priority is to vaccinate as many people as possible as quickly and safely as possible," he said.
He defended the decision to delay the second dose of the Pfizer vaccine by more than the four-week interval being given to patients in England, saying he was simply following the advice given to him by the experts.