England lost the urn in Perth on Tuesday when Australia opened up an unassailable 3-0 lead with a third successive comprehensive victory over the tourists.
Flower's own job, as team director with specific responsibility for the Test team, has therefore come under scrutiny along with the playing futures of several long-established regulars in Alastair Cook's team.
Asked whether he believes he can still take England forward, Flower spoke of "judgments" which must be made by him and his employers, and cast his mind forward only as far as the final two Tests of this series.
It is not beyond the realms of possibility, though, that the face of Ashley Giles - the one-day coach - will start to appear more and often as Flower's reign draws to a close.
When assurances were sought about his future at a press conference in Perth, Flower said: "I've got that judgement to make, and the England [and Wales] Cricket Board will have that to make as well."
His ECB staff contract, amended a year ago to split the roles of Test and limited-overs coach between him and Giles, has no fixed term. There has, however, been a clamour for clarity about his involvement, with former Test opener Geoffrey Boycott among those speaking out within hours of England's third Test hammering.
"I don't plan that far ahead, personally," Flower said. "Obviously, my role means I have to plan ahead for the team's sake, but personally I don't like looking too far ahead.
"Frankly, there are still two Test matches to play in the series and I want all my focus to be on those two Test matches. I think that's the right thing to do for the cricket side."
This Christmas period may be a watershed time not just for Flower, but for a clutch of senior players - wicketkeeper Matt Prior and off-spinner Graeme Swann perhaps foremost - who have fallen well short of their own high standards on this tour. Flower is not about to write anyone off yet, but does hint time is not necessarily on the side of England's thirty-somethings.
"We do have some experienced cricketers and they need to draw on their experience right now to help them through tough periods," he said. "We are going through a tough period as a side now, and a number of those individuals have been going through tough periods in their careers.
"It doesn't mean that their careers are over, but it does mean they need to call on that experience to help them get out of those tough times quicker than other people might."
Prior has is being tracked by a stalking horse in reserve wicketkeeper Jonny Bairstow, and Flower is not ruling out a switch for the Boxing Day Test. "It's a possibility, of course," he said. "Matt Prior has been an outstanding cricketer for England during the second phase of his career. But like with all those positions, we constantly review what our best side will be, what will give us the best chance of winning.
"We have to have an eye to the future as well, so we will meet over the next couple of days and start getting a little clarity on those decisions."
Whoever represents England in the final two Tests will know improvement is non-negotiable after defeats so far by 381, 218 and 150 runs.
Flower said: "When we reflect on the way we've prepared and the way we've taken on the opposition in this series, I think honestly we can say we've been outplayed in every facet."
And he admitted that he would have to shoulder the blame for the poor performances so far.
"Absolutely, it's my responsibility," he said. "So I'm quite comfortable taking that on. Learning from our mistakes is very much a part of our ethos of constant improvement and we need to improve quite quickly."