Goals in each half secured the Bluebirds a third successive win and second place in the table. United, who have won only two of the 18 league games played since Adams replaced Gary Speed in late December, remain bottom, eight points from safety, and are facing football in the third tier for the first time since 1983.
Skipper Craig Bellamy fired home an angled drive that took a deflection off United defender Neill Collins in the 21st minute and substitute Jay Emmanuel-Thomas headed home Chris Burke's cross midway through the second half to seal a comfortable victory for the Welsh side.
A dejected Adams said: "We were second best, no doubt about that. Individually and collectively. To say I am disappointed is an understatement and I apologise to the fans, particularly for the first-half display. Without mincing my words I thought we showed cowardice of the first order."
Teenage substitute defender Harry Maguire offered some hope in the second half, while Stephen Quinn and Matthew Lowton caught the eye.
Adams added: "It's not all doom and gloom from our point of view. It took an 18-year-old boy to come on and put Bellamy on his backside - fairly - three times."
Source: PA
Source: PA