Tiemoue Bakayoko's header 13 minutes from time gave Monaco a 3-1 win on the night at the Stade Louis II and ensured they progressed to the quarter-finals 6-6 on aggregate via the away-goals rule, having lost 5-3 in Manchester last month.
It was the third English scalp Jardim had claimed after he led Monaco past Arsenal at the same last-16 stage two years ago and his side won Group E this time around thanks to a pair of 2-1 wins over Tottenham, who were eliminated.
"I have often dreamt about tonight," Jardim told a post-match press conference. "I think that playing against English teams seems to suit us well.
"We knocked out the second-placed [third] team in the Premier League – this absolutely shows the quality of French football."
Teenage sensation Kylian Mbappe gave Monaco an early lead as the hosts stunned City with an electrifying start and Fabinho made it 2-0 before the break.
Leroy Sane scored in the 71st minute - just reward for the Premier League side's improvement during the second period - but Bakayoko had the final word.
"We did a great first half, where City had no play," Jardim added. "Everybody is happy. We had a great match and we deserve this qualification."