Celtic go into the second leg against AEK with their progress to the play-off round of Champions League qualifying hanging in the balance after drawing 1-1 at home last week.
"I don't want to make excuses", added Rodgers. "Invest in the playing squad".
AEK beat 1967 champions Celtic 2-1 in a fervent atmosphere in Athens for a 3-2 aggregate win over the Scottish side while PAOK held out for a 0-0 draw at Spartak Moscow after edging the Russian outfit 3-2 in the first leg.
Rodrigo Galo scored after six minutes for AEK and Marko Livaja made it 2-0 five minutes after half-time.
Celtic were on the back foot before kick-off, with Rodgers forced to address Dedryck Boyata's absence because of injury or - as is widely presumed - an obdurate reaction to the club's refusal to allow approaches from the likes of Sevilla, Lazio or Lyon and their rejection of a bid from Fulham.
Hoops substitute Scott Sinclair - on for Australia's Tom Rogic - pulled a goal back in the 78th minute but despite a grand finale the visitors could not fashion a second which would have put them through on away goals.
Celtic need to wait until Thursday to find out who they meet in the Europa League.
Pre-match speculation about the fitness of Odsonne Edouard proved well-founded as the French striker and record signing missed out with a knock, with Leigh Griffiths keeping his place.
Manager Brendan Rodgers has refused to say whether Dedryck Boyata has played his last game for Celtic.
Having taken the lead, however, the Greek side simply sat back to defend it.