The small number of newly located votes for the lower house seats of Enfield and Newland would not have affected the results, the state's electoral commission said on Tuesday.
Labor retained both seats by a comfortable margin, followed by One Nation on first preference votes.
"While the operational issues that have occurred have not affected the integrity of the election, I share the community's frustration with these unacceptable system failures," acting South Australian Electoral Commissioner Leah McLay said.
"I want to be perfectly clear that there will be a thorough investigation – both internally and independently - of what led to the problems we've experienced.
"The issues we have experienced fall well short of our expectations – and those of the community."
On Friday, a recount was triggered in the electorate of Narungga after a different batch of lost ballots was located, with One Nation's Chantelle Thomas reaffirmed as winning the seat with a slightly increased margin.
The 81 ballot papers uncounted votes were in three sealed boxes and had been returned to the commission, it was revealed.
While One Nation said it was happy with result, it too backed establishing an inquiry into the conduct of the election.
"We remain committed to establishing a parliamentary inquiry into the conduct of the South Australian election," a party spokesperson told AAP at the time.
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