The Hoops manager at times conducted a verbal battle with some St Mirren supporters behind the dugout during a fast-paced encounter which saw stand-in Parkhead skipper Joe Ledley open the scoring in the fifth minute with a header before a mistake by Celtic left-back Emilio Izaguirre in the 13th minute allowed Esmael Goncalves an easy chance to level.
Anthony Stokes restored the visitors' lead in the 21st minute with a close-range header which, ultimately, was enough to put the Parkhead men into Monday's semi-final draw at Hampden.
Lennon revealed the best exchange of the afternoon as far as he was concerned came when Ledley notched the opener.
"It was from the first whistle really, just a bit of banter really, nothing over the top," he said.
"Nothing new there in Scotland. In fact, the timing of one of the boys' shouts was perfect.
"He said, `Hey Lennon, you will get the sack in the morning' just as Joe Ledley scored, so it was marvellous. I am delighted, we deserved to win the game.
"The equaliser was a comedy of errors and we have to stop doing that. We were so much in control of the game, St Mirren did nothing to warrant them getting back into it and we gift-wrapped them the goal. But our recovery was excellent."
The former Celtic captain praised goalkeeper Fraser Forster for his save from Saints substitute Graham Carey's free-kick late in the second half.
"Fraser made a fantastic save," Lennon said. "Graham is very good at that and he was aware of what was coming. But we could have wrapped the game up by then. Their keeper (Craig) Samson had a great save as well but we deserved to win the game."