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.”
Colchester will hand late fitness tests to Ryan Jackson and Brandon Comley prior to their clash with Yeovil.
Arsenal secured their place in the quarter-finals of the Europa League following their 3-1 defeat of AC Milan at the Emirates Stadium on Thursday.
Danny Welbeck scored twice against AC Milan to toast his England recall by sending Arsenal into the last eight of the Europa League.
Ipswich striker Joe Garner will not play again this season after it emerged he suffered a fractured skull against Sheffield United last week.