Celtic went into the second leg confident of getting the job done in front of their home fans after securing a 1-1 draw in Romania.
To bow out before the group stage even gets underway is a crushing blow, with Europa League football now on the horizon for Celtic.
Lennon defended his decision to deploy Callum McGregor as a make-shift left back in Tuesday's crucial encounter, but admitted his team conceded "crazy" goals as they crashed out.
All it did was highlight the absence of Kieran Tierney, following his move to Arsenal, and display a lack of faith in new signing Boli Bolingoli-Mbombo.More news: Jack Leach says call-up for Ashes can only be win-win situation
James Forrest, hero of the first leg, levelled the scores before Odsonne Edouard made the most of haphazard defending to make it 2-1 to the Scottish champions. We weren't physical or aggressive enough and certainly didn't work hard enough to stop crosses, second balls. You've got to do the basics well - you've got to stop crosses, close people down, get your head on things - and it was nearly as if we scored and wanted to switch off.
"At half-time we got after them a little bit and got the right response but we shot ourselves in the foot with the goals we conceded".
There was to be more drama, however, as Omrani turned in a rebound to make it 4-4 on aggregate and give the visitors the edge on away goals.
"But we needed that two-goal cushion".More news: P'pines to 'fire off' diplomatic protest over Chinese survey ships, warships
"We had enough chances to win the game but we wasted 45 minutes".
"Just to get Olivier Ntcham in midfield because he has been playing well and to have a couple of technicians on the field as well", he said. "We are going to have to accept the criticism that comes our way whether it be from the media or our own supporters or elsewhere".
"I never expected that".
That was Eduoard, who scored and set another one up, but could not stop Celtic from exiting the competition much earlier than they would have liked.More news: Disney Exploring Sequel to Live-Action 'Aladdin'