"I'm sure we'll talk about why our head of government isn't here," Mr Costello told AAP.
"A lot of nations are rather surprised our head of government isn't here."
Mr Costello said it was a mistake for Mr Rudd to have called the election for Saturday.
"This is Australia's opportunity. The levers we can pull (as a country) are very weak compared to the global levers the G20 represents."
Senator Carr arrived in St Petersburg on Wednesday morning on the train from Moscow.
He met with the general secretary of the International Trade Union Confederation, Australian Sharan Burrow, and new WTO director-general Roberto Azevedo, before scheduled evening talks with his Chinese counterpart.
Mr Costello argues if the G20 is really about global governance a peace conference proposed at the G8 in June needs to be back on the agenda.
"A retaliatory strike (against Syria) is just a message," he said on Wednesday.
"It's not going to end the war - it'll probably kill more innocent people."
The World Vision chief is part of the Civil 20 (C20) which, along with the Labour 20 (L20) and Business 20 (B20), channels policy ideas to the main forum.
Mr Costello said the summit must focus on jobs and sustainable, inclusive growth.
If only rich countries grew, he argued, social dislocation and pain among poorer nations would impede trade and subsequent global growth.
The G20 was profoundly important because it included poorer countries such as India, China, Brazil and Indonesia.
"Because you have them sitting at the table you can actually devise development policies that are inclusive," Mr Costello said, before labelling the G8 "a rich man's club".
Ms Burrow, part of the L20, says although Australia's economy is looking "very healthy" compared with the rest of the world, a recent confederation global poll showed people were losing trust in institutions.
Some 80 per cent of people world-wide think governments haven't done enough to tackle unemployment while almost 60 per cent believe their family income has fallen behind cost-of-living rises.
"Unless we do something about social protection, job creation and inclusion of young people through scaling up apprenticeships then, while Australia looks healthy at the moment, it's not an island," the trade union official told AAP.
"You can't operate on your own forever."
Ms Burrow said the G20 shouldn't be a talkfest but rather governments needed to commit to increasing investment, formulating a jobs plan and meeting targets.
- AAP
