Veteran striker Marco Streller scored a poacher's goal after Liverpool failed to deal with a 52nd-minute corner on Wednesday. Martin Skrtel headed back towards his own net and Simon Mignolet could only palm the ball into the striker's path.
The visitors put in another patchy all-round performance after only scraping past Ludogorets at Anfield with a 2-1 triumph courtesy of Steven Gerrard's injury-time penalty.
Now Liverpool must take on holders Real Madrid at home and away knowing they need to pick up points if they are to make it through the group stage.
"We never started great and I don't think we were technically very good tonight," Rodgers told Sky Sports. "Once we got going we created a few chances and possibly did enough to get something from the game, but we defended very, very poorly for the corner.
"It's becoming a symptom of poor defending for us, as it's not the first time. So it's very disappointing that we couldn't get something and the game's decided by a poor defensive corner.
"It's something we continue to talk about, look at and analyse, but you have to deal with it on the field. The key to defending is that you've got to win your first contact on the ball and we continually don't do that enough - and eventually they get a goal."
Liverpool had the ball in the back of the net three times themselves, twice from Raheem Sterling and once by Mario Balotelli, but the offside flag was up on each occasion.
With the Merseyside outfit also struggling for form in the Premier League, Gerrard cut a frustrated figure following this setback.
"I think we created a good few openings where you'd expect us to go on and score, but we didn't deserve anything out of this game and I thought we were too soft all over the pitch," said the skipper.
"I thought they wanted it more, which is very disappointing. Conceding again from a set-piece also isn't good enough, so we need to get it right - you're not going to win football matches if you keep conceding from set-pieces.
"We were second best against just an okay team - we made it easy for them. We wanted something out of this game, I expected us to win, so it's very disappointing.
"There were positive signs against Everton [in a 1-1 draw on Saturday], but we were back to where we've been for much of the season here, which isn't good enough."
Balotelli plugged on gamely as a lone striker but has now netted just once in seven appearances since joining the club from Milan.
"He needs to do more," admitted Rodgers. "Mario will be judged by what he creates and what he scores and he didn't score - but the boy is trying and he is working hard."
