The French Ligue 1 champions recovered from going a goal behind to an Emil Forsberg strike on 32 minutes when Youri Tielemans equalised just two minutes later at the Red Bull Arena.
Monaco had to settle for a point in their opening game of the tournament, but Jardim was satisfied with the performance, despite feeling there is more to come from his side.
He said: "Disappointed? We always come to win matches, of course. But we played with our squad. Every year it's a new story, a new team.
"There's no need to compare with us with the Monaco from last year. We knew this Leipzig team well, we knew they had a lot of physical impact. We put together an 11 to deal with it, also putting some physicality into the game, and it worked well.
"But Leipzig kept their whole squad together from last year, they know how to play together perfectly, whereas we have been integrating players for a few days. But we have a lot of room for improvement."