The Hoops had performed well only to lose 2-0 to AC Milan in their Champions League Group H opener in the San Siro on Wednesday night but they responded with a first-half blitz of the Perth side at Parkhead, easing into a comfortable interval lead through goals by Finnish striker Teemu Pukki, making his first start for his new club, and midfielder Charlie Mulgrew.
The second half was mostly a non-event until Saints substitute Liam Caddis, on for David Wotherspoon, bundled in a Dave MacKay cross with nine minutes remaining before another St Johnstone replacement, Stevie May, hit the post in added time with the Hoops hanging on for the final whistle.
The victory took Celtic to within one goal of league leaders Inverness and the Hoops boss was in no mood to complain about how they got there.
"I'm not going to let the last 10 minutes detract away from what was for the first 80, a top performance," said Lennon.
"For me, it was a natural course of events after midweek. There was mental and physical fatigue in the last 10 minutes which was totally understandable.
"We had no time to prepare for this game at all. It was all about recovery from Wednesday.
"I thought the first half we were fantastic, the best we've played this season and it was after a big Champions League game in midweek, so I take my hat off to the players, it is a big, big win.
"There was a flow to us, we were creating good chances. Anthony Stokes got one off the line, he flashed a shot wide, he looked half-decent on the counter attack.
"But 2-0 is obviously a funny scoreline. If St Johnstone get one then it is all hands to the pump as it were but as I said, I won't let the last 10 minutes affect what was for me, a very good performance."
Lennon, who revealed that right-back Adam Matthews went off at the break with a tight hamstring and an ankle knock after a terrific first-half performance, described as "rubbish" St Johnstone's penalty claim at 2-1 when striker Steven MacLean was challenged by Stokes.
The former Celtic skipper said: "It was never a penalty. Steven has a tendency to go down easy at times."
St Johnstone boss Tommy Wright retorted: "If he (Lennon) is indicating it was simulation, I have never known him (Steven) to be booked for that and players do tend to go down under a challenge.
"I thought it was a free-kick, I couldn't see if it was inside the box from where I was but I thought it was a foul.
"Steven said he had no reason to go down and he is an honest lad.
"There is no chance it was a dive. I don't know exactly what Neil said but I have a golden rule, I don't comment on opposition players, maybe Neil shouldn't comment on mine."
Wright claimed his side could have taken a point following their positive end to the match.
He said: "We didn't work hard enough in the first half. I don't know if the players showed them too much respect.
"I thought we were much better in the second half and truth to be told, we could probably grabbed a draw at the end."
Wright, though, took umbrage at being quizzed as to why May, one of Saints best players this season, started on the bench.
He said: "We were doing well before we brought Stevie on.
"There is no issue. I didn't pick him. That's the team I put out against Rosenborg, aside from Nigel Hasselbaink for Chris Millar. Because Stevie May was left out you want to make an issue, there is no issue."