Video report by ITV News Political Correspondent Shehab Khan
The First Ministers of Scotland and Wales have criticised the UK government's "shambolic" handling of quarantine rules for travellers returning to the country.
Ms Sturgeon said her government would not be "dragged along in the wake of another government’s, to be quite frank, shambolic decision making process".
While Mr Drakeford described dealing with Boris Johnson's government on the matter as "an utterly shambolic experience".
It follows the scrapping of the 14-day self-isolation policy for people returning to or visiting England from certain destinations.
Under the changed proposals, travellers returning from countries such as Spain, France, Italy and Germany will no longer need to self-isolate for two weeks.
When asked about the changes, Mr Drakeford told a press conference in Cardiff: "If ever there was an example of making an announcement first and then trying to work out what you meant by it - that is what we have seen since this announcement was first trailed in the press.
"And day after day we have attempted to get a sensible answer from the UK government on how they intend to make these changes [...] I just have to say it’s been an impossible experience to follow."
Mr Drakeford added that he has "lost track of the number of weeks" that have gone by since he last had direct contact with Mr Johnson.
He added, however, that the way the issue of air bridges had been handled was "the exception and not the rule" in terms of relations with the UK government.
Striking a similar note, Ms Sturgeon said it had been "really quite challenging for Scotland to come to a position" on UK government proposals on lifting quarantine restrictions.
She said there were "difficult and complex" decisions to be made.
Speaking at the Scottish government's daily coronavirus briefing she added:
"Just to illustrate the point (on) the shifting sands of the UK government's position – the list of countries that they were yesterday demanding that the Scottish government sign up to, and suggesting we were a barrier to getting an agreement on, is not the same as the list they have shared with us today."
Ms Sturgeon said it was now "likely, very likely" that her government would "be able to agree the list of countries the UK has categorised as low-risk" but added "we will need to do a proper assessment of that."
Speaking on Friday morning, Transport Secretary Grant Shapps told ITV that the government had been "really careful and cautious" in bringing in exemptions to the quarantine rule.
In response to the criticisms made by both First Ministers, a UK government spokesperson said: "We have been working with all devolved administrations on quarantine from the outset and we will continue to do so.
It is for the devolved administrations to make and explain their own decisions and the measures they're putting in place.
It concluded: "Air passengers arriving in airports in England should ensure that they follow the guidance from the relevant devolved administrations in the area where they live."