Geoffrey Kondogbia's deflected strike put the Ligue 1 side in the lead before Dimitar Berbatov doubled their advantage, and though Alex Oxlade-Chamberlain pulled back a late goal, Yannick Ferreira Carrasco struck a third in the dying moments.
Jardim praised his side for nullifying the threat of the Gunners' attacking stars - but says the victory was not the most important of their season so far.
"It's not our biggest Champions League win. We also beat Zenit and [Bayer] Leverkusen. The one in Germany was most important as it allowed us to qualify for the second round," he told reporters after the match.
"Arsenal were very strong in the first half and then they suffered a little. In the first half, we were very strong defensively and then took advantage of the spaces.
"Arsenal have excellent individuals, but this is a team sport and we were able to render them harmless. We were very organised, but also able to attack with quality.
"Nobody thought this was possible, and we did it. But the task in the second leg still remains.
"We've won nothing yet, we just took an advantage. Football is also art - you have to know how to attack, how to defend. My team is very balanced."
Jardim reserved special praise for the all-round efforts of Berbatov - a player who has attracted criticism throughout his career for his languid style.
"In terms of positioning and defensive work, Berbatov was tremendous," he added.