Mbappe and resurgent forward Radamel Falcao scored early goals to put immediate pressure on Dortmund, which trailed 3-2 from the first leg of the quarterfinal in Germany.
Dortmund's plight in Monaco was not helped by Tuchel's decision to play Erik Durm, who has just returned from injury, on the right wing, which proved to be a disaster.
But Mbappe is confident Monaco can deal with the contest regardless of who they get, rising to the occasion to make their first final since the team of 2004 who lost out to Jose Mourinho's Porto.
The Germany global was dragged off after only 26 minutes as Monaco had attacked freely down his channel and raced into a 2-0 lead through goals by Kylian Mbappe and Radamel Falcao.
The visitors had an excellent chance to level the score in the 14th minute when Nuri Sahin free kick beat Monaco goalkeeper Danijel Subaić but it did not beat the post.More news: Kompany scores as Manchester City climb to third with Southampton victory
However, any hopes the Germans had of staying the competition were snuffed out when Monaco sub Valere Germain netted late on, just 22 seconds after coming off the bench.
Jardim, though, believes the Principality club, who are the first Ligue 1 side to reach the last four of the competition since Lyon in 2009-10, still have it all to do when taking on the European elite.
"At this level you can not set limits for your players. France isn't used to having teams reach this stage of the competition".
"All the players played at a high level", Jardim said. We have made great games with a back three, especially in the Champions League, but we were not good enough.
"Our rivals will want to draw us (on Friday) but our ambition is to enjoy it and play with our attacking qualities like we always do".More news: Oracle Buys Digital Measurement Specialist Moat
"Everyone was on the bus and the police were ready to accompany us, but then we were told we had to wait", Tuchel said.
Thomas Tuchel has admitted his Borussia Dortmund side simply weren't up to scratch as they crashed out of the Champions League.
Before kick-off, the home fans showed solidarity by unveiling a banner which read: "BVB: You Will Never Walk Alone" as the anthem played out around the Stade Louis II.
Dortmund coach Tuchel had few complaints, telling reporters: "We started well with one or two risky moves where we found some space and then conceded an unlucky goal". After every step we've taken we've looked at it and we've kept working.
"We said at the half-time break that we could still score three in the second-half, but their third goal was a knock-out (punch)".More news: Pence In South Korea, Visits DMZ And US Troops
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