Mr Grandi told SBS that he raised several issues with Mr Dutton during their meeting and before President Obama’s invite-only side summit on refugees, including the "situation in Nauru and Manus Island".
“We reiterated our point that it is important to find solutions, especially given the very dire humanitarian situation in those two areas” Mr Grandi said.
The criticism comes less than a day after Prime Minister Malcolm Turnbull declared Australia’s border security “the best in the world".
“For us offshore processing of asylum has some problematic aspects, we’ve always said that, we’ve said it very openly," Mr Grandi said.
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“The strong focus in Europe, in Australia and in North America has really been on security and control.
“That’s really only looking at the problem at the end of the process.
“We really need to look at the root causes of the problem and we need to address them.”
Despite opposition from presidential candidates Hillary Clinton and Donald Trump, Mr Turnbull once again urged the US Congress to pass the Trans-Pacific Partnership trade deal.
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Australia’s Ambassador to the US, former treasurer Joe Hockey has been leading the lobbying effort in Washington DC.
“There is a fair degree, I’d say only a fair degree of optimism that it will be ratified during the lame duck period,” Mr Turnbull said.
Australia’s hopes now rest on congressional approval for the deal after the November election and before President Obama leaves the White House in January.
“It will be a lot harder to do afterwards,” Mr Turnbull said.
“This is a window of opportunity and I believe it will be in America’s long term interests, as well the rest of the Asia Pacific, and especially Australia’s, for them to ratify it.”
