Media playback is not supported on this device
Campbell, who won a bronze medal in the event at London 2012, was fourth in his semi-final in Rio with only the first three going through to the final.
Northern Irishman Campbell, 33, led early on but dropped back after being passed by New Zealand's defending champion Mahe Drysdale.
Campbell is expected to retire from the sport after these Games.
The Coleraine man is the first Northern Ireland competitor to compete at a fourth Olympics.
Drysdale took victory in seven minute and 3.70 seconds ahead of Belarusian Stanislau Shcharbachenia (7:06.69) and Belgium's Hannes Obreno (7:06.76) who took the last qualifying place ahead of Campbell.
The Northern Irishman, who was almost three seconds off qualification as he clocked 7:09.54, will have to content himself with a place in the B final.
Campbell's fellow Coleraine men, the Chambers brothers, also failed to qualify for the finals of their events in Rio.
Richard and Peter Chambers helped Britain win silver in the lightweight fours at London 2012.
Meanwhile, Irish pair Sinead Lynch and Claire Lambe finished sixth in the women's lightweight double sculls final.
The Irish duo dropped off the pace early on and their time of 7:13.09 left them almost seven seconds outside the medals.
Coleraine rower Alan Campbell has missed out on a place in the single sculls final at the Olympic Games.