Her comments came as Mr Johnson is expected to announce on Monday the lifting of the legal requirement for Covid self-isolation in England and free testing.
The Scottish government believes that quarantine should remain for those who have the virus, along with large-scale free testing.
The new Covid strategy for Scotland will be announced Tuesday at Holyrood.
Speaking on Monday morning during a visit to Social Bite in Edinburgh, Ms Sturgeon said: “We are once again sharply reminded of this illogical position that the governments of Scotland, Wales and Northern Ireland have to deal with. health care decisions in our own countries, but it’s the Treasury that makes the funding decisions, and they only seem to be driven by the decisions that Boris Johnson makes for England.
“It’s unsustainable and unacceptable, but we’re in that situation.”
Scotland needs to be consulted if the UK cuts Covid testing capacity, says Humza Yo…
The first minister hopes it will become clear on Monday what the remaining funding for testing will be.
It is understood that the Covid cabinet meeting was postponed on Monday due to a dispute over the running costs of free testing, which is backed by Sajid Javid but not backed by Rishi Sunak.
Ms Sturgeon said she “expressed her disappointment” to Michael Gove that the Scottish government still does not know the decision the UK government will make and the delay “makes it worse”.
Ms Sturgeon said: “If Sunak wins, the issue will not only be stopping free access to testing in the short term (a decision I disagree with). long-term follow-up and response to new options”.
She added: “Presumably England is not going to completely withdraw its test infrastructure, so what will be the residual funding and what will it allow to support autonomous administrations.
“This would be unacceptable now, as it has been in the past, as the decisions that the Scottish Government or the governments of Wales and Northern Ireland consider right on public health grounds are limited by funding decisions that the Treasury makes only on the basis of what is decided for England”.