It came just four days before a meeting with Spartak Moscow in the Champions League that will determine whether the Scottish champions progress to the knockout stages for only the third time. Yet Lennon, no doubt due to the fact he rested so many players who will have key roles to play against the Russians in midweek, reacted calmly to this latest embarrassment.
"We missed a hatful of chances and should have seen the game off," he said. "The longer the game stayed 1-0, the greater the likelihood became that they would equalise and that is what happened. We will move on.
"This will not impact on Wednesday night whatsoever. We will have a different team, there will be different opposition, there will be a different atmosphere and there is a different prize at the end of it. The players will be fully focused and we are hoping to get a different result."
Arbroath's players will, however, long remember what is one of the most remarkable results, if not the most remarkable, in the 134-year history of the Gayfield Park club.
Player/manager Sheerin, who starred for Inverness Caledonian Thistle when they famously defeated Celtic at Parkhead in this competition back in 2000, certainly rated it as the best result of his lengthy career.
"It probably outweighs what I did with Inverness," he said. "We were a full-time football team back then. But Arbroath are just part-time. To get a result against the Scottish champions away from home is just incredible."
Fraser Forster and Gary Hooper started on the bench for Celtic while Kris Commons, Joe Ledley, Mikael Lustig, Georgios Samaras and Kelvin Wilson were all absent from the squad.
However, Lennon still fielded millions of pounds worth of talent – with Efetobore Ambrose, Scott Brown, Adam Matthews and Victor Wanyama all in the starting line-up.
At times Arbroath played with six across the back, three in midfield and just one man, Derek Holmes, lurking upfield. That ultra-defensive set-up proved difficult for Celtic to break down.
When they finally opened the scoring it was in a bizarre manner. Stuart Malcolm dispossessed Miku Fedor inside his own penalty box on 36 minutes and attempted to clear. The ball, though, immediately deflected off his unsuspecting team-mate Alex Keddie, spun past the helpless Scott Morrison, and into the net.
Miku looked the likeliest candidate to score a second for Celtic to put the outcome beyond doubt. He was denied only by the woodwork and the brilliance of Morrison.
The lack of ruthlessness in the final third displayed by the home team made the astonishing finale almost inevitable. The maroon-clad hordes, who packed out the away section, enjoyed their day out and then some. They grew more vocal as the game progressed and the possibility of their side causing an upset increased.
"Champions League? You're having a laugh!" rang out around the stadium as the game entered its closing stages. When Thomas Rogne fouled Holmes and conceded a free-kick on the edge of the area in 87 minutes, it gave the visitors the opportunity they needed to draw level.
Steven Doris unleashed a powerful shot that took a deflection off the defensive wall and arched beyond Lukasz Zaluska and into the goal. His defence's failure to face up to the shot did not go unnoticed by Lennon.
"I learned I can't have a couple of people in the wall because they seemed to jump out of the way," he said. "That annoyed me more than anything. That is where the deflection came from. If they had stood their ground it wouldn't have happened."
Lassad Nouioui had replaced Tony Watt shortly before that and the Tunisian striker nearly snatched a victory in the final minute.
His left-footed volley was heading straight for the top-left corner of the goal but the fingertip save that diverted the shot over was Morrison's best of the day.
From bad to worst