Celtic suffered a 2-1 defeat to AEK Athens this evening that now sees his side slip into the Europa League.
The Scottish champions were the heavy favourites to progress beyond the third-qualifying round after drawing 1-1 in the first leg.
However, goals from Bito Rodrigo Galo and Marko Livaja either side of the break saw Celtic fail to book a spot against Malmo or MOL Vidi in a play-off to reach the group stages.
Celtic had been looking to make it to the Champions League group stage for the third year in a row but despite Scott Sinclair’s goal to push for a comeback they ultimately fell short.
“We’ve got to stop the cross for the first and the second is poor defending,” Rodgers said.
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“We gave ourselves a chance and threw everything at it.
“I thought a lot of our build-up play was worth something from the game but you can’t defend that softly.
“I still felt this was a game in which we had more than enough to win but you have to defend better than we did.
“We gave AEK a lot of problems but you have to defend properly and we didn’t do that.”
The 70,000-capacity stadium was only around half-full but the home fans roared when Niklas Hult, at the second attempt, got his cross pass fellow Swedish defender Mikael Lustig to Brazilian midfielder Galo, who swept it past keeper Craig Gordon from 12 yards after six minutes.
It was the start the Parkhead side had feared and moments later they almost conceded a second when Victor Klonaridis, who scored in Glasgow last week, burst into the Hoops box but toe-poked a shot wide of the target from eight yards.
Having taken the lead, however, the Greek side simply sat back to defend it.
Celtic took control, with Tom Rogic and Griffiths both having luckless efforts on goal before the latter sent a fine Callum McGregor cross inches past the post from eight yards.
Hendry headed a Griffiths corner over the bar just before the interval but any positivity Celtic’s response elicited evaporated early in the second half when Galo’s free-kick to the back post was headed back across goal by Vassilis Lampropoulos for Livaja to head past Gordon.
Celtic need to wait until Thursday to find out who they meet in the Europa League. Spartaks Jurmala go to Suduva trailing 1-0 from the first leg, so the Lithuanians will be big favourites.