The Scottish champions trailed 4-1 from the first leg of their third qualifying round tie and were unable to stage a fightback as they were defeated 2-0 at Murrayfield on Wednesday.
It is the first time in three seasons that Celtic have failed to make it into the main draw, which is not the start to his tenure that manager Ronny Deila had in mind.
The Glasgow outfit came into this tie knowing they needed to attack from the off, but they fell further behind when a quick break and a ball over the top sent Michal Zyro - a scorer in the first leg - through on goal and the midfielder stroked the ball beyond home goalkeeper Fraser Forster.
That 36th-minute effort left Celtic requiring four goals simply to force extra time, and the result was put beyond all doubt one minute after the hour-mark when Michael Kucharczyk rounded Forster and applied the finish.
Celtic will now drop into the UEFA Europa League, but the lack of top-level continental competition may prompt clubs clubs to move for their prized assets such as Forster and Kris Commons,
Besiktas came into the home leg of their clash with Feyenoord holding a 2-1 lead, and Demba Ba's hat-trick saw them sail into the play-off round as they triumphed 3-1 in the second leg.
After opening the scoring in the 28th minute, former Chelsea striker Ba found the back of the net twice in the space of six second-half minutes late on.
Malmo equalled their best Champions League performance in the modern era by reaching the play-off round with a 2-0 victory over Sparta which made it 4-4 on aggregate and ensured they progressed on away goals.
Zenit and Steaua Bucharest guaranteed their places in the next round with wins over 10-man opposition in the shape of AEL and Aktobe respectively.
A red card also ended Sheriff's chances of going through as they were held to a goalless draw and lost 2-1 on aggregate to Slovan Bratislava, and Partizan ended the match a man light as a 2-2 draw against Ludogorets saw them eliminated on away goals.
An Anders Jacobsen brace turned Aalborg's first-leg deficit into a 2-1 aggregate triumph over Dinamo Zagreb, while Copenhagen were another Danish side to progress courtesy of a 2-0 win against Dnipro.
Elsewhere, APOEL's 2-0 win over HJK saw them through as 4-2 victors, and Red Bull Salzburg came from 2-1 down to progress 3-2 against Qarabag.
