Thomas Lemar and Adama Diakhaby bagged the goals for the principality side while Alassane Plea was on target for Nice at the Allianz Riviera in the 2-1 success.
The remaining last-eight ties take place on January 10 as Rennes take on Toulouse, Amiens entertain Paris Saint-Germain and Angers host Montpellier.
But Monaco can sit back and relax with their last-four place secured and Jardin felt there were only positives to come out of the quarter-final triumph.
"It was important for two reasons: because we have qualified for the semi-finals and it was an objective of ours to go as far as possible in this competition, and because it was a derby and so it was important for our supporters," he told the Ligue 1 website.
"It has not gone well here the last couple of times. Today was hugely satisfying. The last couple of times here we played with a bit too high a line.
"Nice played on the counter-attack. Today we defended deeper to avoid their quick breaks. We used a different approach to get our two goals. It is to be expected that we are stronger with the injured players back. We have a competitive squad to enable us to play every three days."