After 120 goalless and dull minutes at Stade Louis II, Nabil Dirar fired his effort against the crossbar, paving the way for Sebastien Squillaci to seal a memorable victory.
The defeat meant Monaco have not reached the decider of the Coupe de la Ligue since they won the competition in 2003 and Jardim conceded the three-time finalists were below their best against Bastia.
"I'm disappointed because the goal was to play the final at the Stade de France," Jardim said afterwards."We have not won, so our mindset is disappointment.
"I think we tried to produce more game than the opponent, who made a good match physically. They showed more intensity and aggressiveness than us, that's why they won.
"They also won many duels, I congratulate them. But it's more difficult to play with the ball than defending, keeping its position as Bastia did before to create chances at the end of overtime.
"Now our goal is to continue to work to go far in all three competitions we have left."
Squillaci came back to haunt his former club as he tucked the ball past Monaco goalkeeper Maarten Stekelenburg.
The successful spot-kick ensured a showdown with defending champions Paris Saint-Germain, whom they faced in their most recent final appearance in 1995.
"It is a great pride for the people, for the wonderful public, for the 12th man," said Bastia boss Ghislain Printant.
"In the end, I think the most enterprising team won and deserved to go to the Stade de France. I am proud of my players who surprise me at every opportunity."
