Lennon's men ended a horrific three-year run of losing form against the SPL champions with a 3-2 victory at Hampden Park to set up a March final against Hearts.
They led through debutant Esmael Goncalves but were indebted to a missed penalty by Charlie Mulgrew to stay level before a quick two-goal salvo by Paul McGowan and Steven Thompson that sent them on the way to victory.
"We're absolutely delighted," Lennon said. "I think this week it's been a fantastic effort from the backroom staff, with the preparation for the game, the tactics we've worked on.
"(The players) had the belief and showed their true potential. They can bring that to any game.
"It's a fantastic achievement and fantastic result, but more important was the manner in which they've got the result. That's for all our fans out there who've stuck by us through thick and thin."
A delighted Thompson added: "We knew we could cause Celtic problems and we did. It's a magnificent feeling. I think there was (belief beforehand). I felt it this morning on the bus, in the changing room. I think the first 10 minutes gave us a lot of belief.
"We created chances, scored the goal - these things give you great belief. I think it had been so long since we scored against Celtic that it just gave us the belief that we could do this."
And McGowan said: "We've not played well against Celtic every game. We haven't scored since I've been here against them. That was another plus. We just knew it was a cup game and anything could happen.
"All credit to the boys - we showed great character. It's a great day for the club, for the supporters. We fear no-one. We know how good we can be. We're not always consistent enough but if we take that into the final I'm pretty sure we can come away with the cup."