Greene ran a smart race in a tightly-bunched field, keeping out of trouble and placing herself well during the middle stages.
She was still in contact with the leaders with 600m to run but could not lift her pace when the African runners put the acid on.
She finished with a personal best of 9 minutes 21.23 seconds.
Greene will also contest the 1500m, starting on Friday.
Whyte produced an outstanding run in his heat of the 400m, finishing third in a new personal best time of 46.62 seconds. It improved the time of 46.73 seconds he set last week. He qualified 13th of the 24 starters for Thursday's semifinals.
Julian Oakley (3.49.43) and Ben Moynihan (3.50.59) were both eighth in their respective 1500m heats and did not qualify for the final. Oakley competes in the 800m later in the week.
Sprinter Kodi Harman was sixth in his 100m heat in a time of 10.99 seconds and did not qualify for the semifinals.
Nicholas Southgate cleared 4.75m in the pole vault but needed to achieve 5.05m to move through to the final.
Defending shot put champion Jacko Gill contests qualifying tonight (NZT) with the final on Thursday morning.
