The Blues, recently dethroned as Premier League champions, needed to beat Newcastle and hope Brighton did the same to Liverpool to finish in the top four.
As expected, Liverpool beat Brighton to clinch the final Champions League spot and finish the season behind Manchester City, Manchester United and Tottenham. Chelsea were thrashed 3-0 by Newcastle.
It will be the first time Chelsea play in the group stages of the Europa League, with their only other appearance in the competition coming after dropping out of the Champions League.
Rafael Benitez was manager on that occasion as Chelsea beat Sparta Prague, Steaua Bucurest, Ruben Kazan, Basel and Benfica to win the trophy.
The last time Chelsea competed in the first round of Europe's second-tier competition was in 2002-03 when they lost 5-4 on aggregate to Norweign outfit Viking.