Having withstood first-half pressure from their hosts, Monaco created some good openings but found Julio Cesar in stubborn mood.
The Brazilian goalkeeper made a fine save from Yannick Ferreira-Carrasco to keep the game goalless, and it proved crucial as Talisca netted the winner for Benfica with eight minutes to play.
Jardim was frustrated by his team's profligacy in front of goal and warned them there will need to be improvements if they are to qualify from Group C.
"There is disappointment," he admitted. "Victory does not reflect what happened, it's a matter of efficiency.
"Benfica were more effective than us.
"Regarding the qualification, everything is open, we can still qualify.
"We have young players who are not experienced strikers. They need to work to improve."
Monaco face Bayer Leverkusen in the next round of fixtures, with Zenit and Benfica now just a point behind them with two games to play.
