The North statement contradicted the version of events given by Pompeo just hours before. He had said progress was made during the talks. It was the first time he had visited North Korea since the Donald Trump-Kim Jong-un summit.
The North's spokesman said: "We expected that the US side would come with productive measures conducive to building trust in line with the spirit of the North-US summit and (we) considered providing something that would correspond to them.
"The US just came out with such unilateral and robber-like denuclearization demands as CVID, declaration and verification that go against the spirit of the North-US summit meeting," he added, calling the talks "really disappointing".
CVID stands for complete, verifiable and irreversible dismantlement of North Korea's nuclear programme, an oft-cited demand by Washington for Pyongyang.
The spokesman apparently rejected the US demand and reiterated Pyongyang's call for a "phased" and "synchronous" approach, saying that it would be the shortest way to realize a nuclear-free Korean Peninsula, Yonhap news agency reported.
"It would be the shortest path towards realization of the denuclearization of the Korean Peninsula to ... boldly break away from the failure-ridden methods of the past, push for whole new approaches and seek to resolve problems one by one based on trust and in a phased and synchronous principle," he said.
The spokesman said that the first high-level talks between the two countries following the summit failed to consolidate mutual trust, only to risk undermining the North's commitment to denuclearization.
However, he emphasized that the North still has trust in the US President, apparently hinting that Pyongyang wanted to keep the ongoing denuclearization talks on track.
The official also mentioned that Kim Jong-un's letter for Trump was given to Pompeo, saying that he voiced confidence that the trust and friendship built through the Singapore meeting will deepen through talks that the two countries will have going forward.