Yesterday's display of weaponry in Seoul was the largest for a decade, involving 11,000 troops, 120 aircraft, tanks, heavy artillery and a range of missiles.
Although North Korea regularly stages far larger military parades in Pyongyang, it took exception to what it saw as a provocative, confrontational exercise.
"The puppets staged an unprecedented display of lunatic hostility," said the official ruling party mouthpiece, Rodong Sinmun.
The newspaper said the parade was aimed at strengthening "military collusion" with the United States and "spurring preparations to attack the North".
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Hagel was on a visit to underscore US commitment to its military alliance with South Korea, where 28,500 US troops are stationed.
The "confrontational circus" yesterday showed the true nature of South Korea and the United States as "destroyers of inter-Korean dialogue", the Rodong Sinmun said.
The parade marked the first public outing of a new high-precision cruise missile, the Hyeonmu 3, which military officials say is capable of targeting the office windows of North Korean leaders.
In her keynote speech at the military display in Seoul, President Park Geun-Hye warned of the "very grave" threat posed by Pyongyang's nuclear weapons programme and stressed the need for South Korea to develop a sophisticated deterrent capability.