The selections of Head, Cameron Green and Carey were all critiqued at various points over the past two months.
But Head and Green, under pressure from Usman Khawaja and Mitch Marsh respectively last month, entrenched themselves in the Australian Test XI after playing key roles in a dominant 4-0 series win.
Carey's position has triggered more debate but the wicketkeeper signed off with his most impressive performance of the summer, scoring 49 to prop up a second-innings total of 155.
The South Australian also did well to pouch edges offered by Chris Woakes and Zak Crawley amid England's calamitous collapse of 10-56, having invited scrutiny earlier in the series with a couple of dropped catches.
"All in all, he's had an exceptional series," Head said of Carey.
"He's batted in some tricky situations, we take a lot of confidence from that.
"He showed moments throughout the series, how dangerous he could be at seven.
"He works extremely hard.
"I know he's disappointed that he let a couple chances go. I felt like he kept beautifully throughout the series and that (consistency) highlighted a couple of (erroneous) moments."
Carey became the first Australian male keeper to make a Test debut on home soil since Adam Gilchrist.
It came after a long-term apprenticeship in limited-overs cricket but also rapidly and unexpectedly, following Tim Paine's sexting scandal.
Carey's return of 183 runs at 20.33 does not read well.
But that includes scores of six and zero, coming on the cusp of declarations, plus a knock of nine while opening in the absence of an injured David Warner in Brisbane.
"He's had to play the team role. One thing I know about Alex is he's such a team player," Head said.
"He's a selfless player ... the team absolutely love playing with him.
"He's my best mate, so I want to see him do well.
"He got a little bit of luck (in Hobart) ... (it was) deserved for the series he's had."
Head, named player of the series after topping the run-scoring charts despite missing the fourth Test because of COVID-19, also heaped praise on Green.
"To maybe be questioned a little bit throughout the series," Head said.
"For a young guy, who hasn't played a hell of a lot of Test cricket and still not a hell of a lot of first-class cricket, to take that on board.
"Work on his game and get the results over the last three Tests just shows the character he is."
15°C