They were not the only high profile casualties as last season's quarter-finalists Monaco exited yesterday despite coming from behind to beat Valencia 2-1 at home -- they have lost just once in their last 12 European club games at Stade Louis II -- but lost 4-3 on aggregate.
Another side who reached the knockout stages last season also failed to get over the play-off hurdle this time round as Basel, who progressed at the expense of Liverpool in last season's competition, exited after a 1-1 draw in Israel against Maccabi Tel-Avi saw the hosts progress on the away goals rule, the tie finishing 3-3 on aggregate.
The cost to Celtic may be felt immediately as it could prompt talented defender Virgil van Dijk to jump at the chance of a prestigious move to English Premier League side Southampton.
Celtic manager Ronny Deila, though, is loathe to part with him.
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"We don't have to sell Virgil van Dijk, but you never know in football," said the Norwegian.
"You have to deal with it but we looked very stressed. We didn't look like we wanted to go out and play football. We have a lot of young players coming through but this was a hard lesson for us."
Valencia had all but wrapped up business after four minutes, Alvaro Negredo chipping Subasic brilliantly with the ball going into the far corner.
The hosts, needing three goals to even take it to extra-time, replied almost immediately, Italian defender Andrea Raggi firing the ball past Australian goalkeeper Mathew Ryan from the edge of the area.