The Dragons missed out in their unlikely bid to land a Heineken Champions Cup place despite victory over Edinburgh in their last PRO14 match.
Dean Ryan's side needed to win by 45 points to pip Glasgow and go above them into fourth spot in Conference A and roared into a 24-5 half-time lead.
Matthew Screech grabbed two early tries and Jonah Holmes went over for another as the Dragons went in at the interval with hopes raised.
With Sam Davies on target with the boot, converting the three tries and also kicking a penalty, the Dragons were 17-0 up in as many minutes, Holmes bolstering their tally with his own score in the 33rd minute.
However, the Dragons were unable to score again in the second period with Charlie Shiel and Blair Kinghorn leading Edinburgh's fightback with tries, after Mesu Kunavula had scored earlier on for the visitors.
The Dragons did at least hold out for victory despite Edinburgh pressure near the end and head into next weekend's Challenge Cup quarter-final clash against Northampton with some momentum behind them.
The Dragons finished fifth in the table, winning six of their 16 games, with just Zebre below them.
Leinster finished top, also beating Munster in the play-off final, with Ulster second, Ospreys third and Glasgow fourth.
