Janet Cooke, a Washington Post reporter who won a Pulitzer Prize last year for a fabricated report about a young heroin addict, says she made up the story because she had spent two months looking for such a person and ''if I did not produce a story, then how was I to justify my time?''

Miss Cooke resigned in the furor over the article, ''Jimmy's World,'' and The Post returned the prize. In her first public statements since the incident last spri ng, Miss Cooke told Phil Donohue of NB C News that she thought what she had done was wrong.

She contended that there was an ''undercurrent'' of competitiveness among Post reporters ''to be first, to be flashiest, to be sensational.''

''I simply wanted to write a story I had been working on so that I would not have to go back and say I cannot do it. I did not want to fail,'' Miss Cooke said