The Sri Lankans received a significant boost ahead of the Melbourne Cricket Ground match when Ponting said he was withdrawing to attend his grandmother's funeral in Tasmania.
Sangakkara's team hold the whip hand going into the three-match ODI series after thrashing Australia by seven wickets in a Twenty20 match in Perth last Sunday.
The wicketkeeper-batsman warned that Sri Lanka must keep applying the pressure to the world's number one-ranked one-day team.
"A player of Ricky's calibre not being in the side, he's a huge blow to anyone," Sangakkara told reporters.
"He's one of the best batsmen probably in the last two decades or so.
"I'm not sure how it will affect the Australians, but for us again it's a case of thinking more about us and trying to keep a focus on the processes that we try and do setting the tone for the innings and getting our combinations right.
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Although Sri Lanka are using the Australian tour as a buildup to next year's World Cup on the sub-continent, Sa