Celtic's hopes of qualifying for the last 16 of the tournament are long gone, but they are still in contention for the Europa League as they sit third in Group B, three points above bottom-placed Anderlecht ahead of the final round of games.
"It is a sore one," Rodgers told reporters after the defeat. "We conceded seven goals in Barcelona as well but there were lots of moments here where we were very good I felt. You have to admire their quality.
"They always threatened and scored some outstanding goals. I was proud of the players. We are disappointed with the goals we gave away and you can't give away cheap goals at this level. The ball is everything, we gave it away and we were punished.
"But it goes to the final game and we can still qualify for the Europa League. We came here to play against the best of the best. I'd be very surprised if PSG don't make the final of the competition.
"We played five at the back, what do you want me to do? Play seven? Sometimes you have to take your hat off to their quality. Our players ran themselves into the ground but made mistakes."