Ponting's successor Michael Clarke confirmed on Tuesday selectors had decided to retain Peter Nevill as gloveman after Haddin missed the second test to be at his sick daughter's side in hospital.
Like many, Ponting believes the 37-year-old may have played his 66th and final test in the defeat to England in Cardiff which opened the series.
"Hadds has been the heart and soul of the team since taking over from Adam Gilchrist," Ponting wrote in a column in The Australian on Wednesday.
"He is a good gloveman, can be an important batsman and he keeps the team on its toes in the field.
"He is a hard man and renowned for a bit of chirp but if you look closely the last couple of years he generally has a smile on his face. He loves the game.
"He is a broken finger away from recall so this may not be the end for him, but I suspect we won't see him again and I am a little concerned that the team may miss him more than they expect. I hope I am wrong."
Ponting, while conceding that Nevill was a "good keeper" who "looked tidy" on debut at Lord's without being "exceptional", said Haddin's contribution with the bat in the 5-0 sweep of England in the 2013-4 Ashes series showed his importance.
"Brad's batting has been critical to the team on many occasions but none more so than in the last Ashes. He scored 493 runs at an average of 62 and was just behind David Warner who scored 523 from two more innings," Ponting added.
"It is in a series like that that his experience and value to the team came through. In the hard moments Brad always seemed to dig in. It is hard to remember him not batting in that series as he was involved in so many important partnerships."
While Ponting was "disappointed" by a decision that did not "sit right" with him, another Australian test great Matthew Hayden was more forthright in his condemnation.
"After the hell he’s gone through, it is outrageous that Brad Haddin hasn’t gotten his spot back for the third Ashes test," the former test opener wrote in a column on news.com.au.
"It doesn't say much for the family-first policy if Brad puts his family first and all of a sudden he's out. Sometimes the heart has to play a part in selection."
(This version has been refiled to fix spelling of 'Edgbaston')
(Reporting by Nick Mulvenney, editing by Peter Rutherford)
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