The Buddies beat Celtic 3-2 on Sunday to qualify for the Scottish Communities League Cup Final and were clearly confident against high-flying Caley Thistle.
Esmael Goncalves and Steven Thompson grabbed the goals with Billy McKay scoring the goal for the visitors just before the break.
Lennon said: "To go out there and continue, more so in the first half, where we left off on Sunday was fantastic and the only disappointment was losing a sloppy penalty on half-time.
"It was a terrific header for the winner from Steven Thompson; we are absolutely delighted that in the matter of three days we have managed to beat the two top teams in the league.
"I thought to a man the guys were fantastic, we played some exceptional football in the first half and the only thing that was missing at times was an end product."