The report noted agencies "should set targets appropriate to their operational context".
"The targets in scenarios ... are for illustrative purposes only and may not feature appropriate targets for each agency.
It also noted the potential savings did not take into account the investment necessary to achieve them.
Finance Minister Bill English said the report was an important tool for state sector chief executives "to understand their organisations properly before they make change".
"It shows back-office costs have been fairly flat in the last year, but there is ample room for future savings. Over the next year, I'd expect agencies to make more back-office savings to free up money for priority frontline services."
But the PSA said the fact that costs had risen by $19 million was proof there was "little left to squeeze out of agencies that have already been cut back to their core".
"Government departments have already found considerable savings to meet targets, so it's no surprise that the anticipated gains from this exercise have not been realised", said national secretary Richard Wagstaff.
"There's little left to cut without hitting services directly and we are already seeing this with a reduction in frontline staff in Departments like IRD, DoC, ACC, MAF, Housing and Mfat.
"The report says there's still huge potential for savings in some departments but this is an overly ambitious claim."