The disappointing reverse left the Hoops 10 points behind SPL leaders Rangers, albeit having played a game less than their cross-city rivals.
Celtic’s championship aspirations suffered a severe blow after second-half goals from Rudi Skacel and Ryan Stevenson gave the dogged Jambos victory in a pulsating encounter.
Skacel broke the deadlock in the 58th minute with an unstoppable drive from the edge of the box, before Kris Commons was shown a straight card by referee Craig Thomson in the 65th minute for a reckless challenge on Adrian Mrowiec.
Stevenson scored a breakaway second 10 minutes from time to leave Celtic in third place behind Motherwell going in to the international break and with their manager worrying about the rest of the campaign.
“It is a concern, obviously,” said the Parkhead boss.
“We have a game in hand but we have to win that game and cut it to seven and eat away at it.
“But we have to find more consistency in our performances.
“We have lost three games already this season and last season we lost four.
“It is a difficult position that I am in but I understand that position.
“The players are going to have to turn it around, and I am going to have to turn it around.
“There are six, seven months of the season to go and we have to find consistency.”
Aside from the defeat, it was the bluntness of their attack that irked Lennon the most.
“My biggest bugbear about today is the amount of chances we missed,” continued the Irishman.
“We missed some really good chances in the first half. We weren’t clinical enough and that was the biggest disappointment.”
Lennon criticised Kris Commons, just back in the side after injury and illness, saying: “One player lost his discipline and let us down badly.
“I didn’t get a good look at it but from what I can gather it was a lunge and it is high.
“He came in and held his hand up but it is too late.”
Rangers sit nine points clear of second-placed Motherwell — following Saturday’s 1-0 win over Hibernian.
Kyle Lafferty grabbed the only goal of the game. The Northern Irishman netted in the second half after Steven Whittaker missed from the penalty spot just before half-time.
Motherwell were 3-1 winners at Dundee United while Inverness are just a point behind Dunfermline at the bottom of the table after they came from behind to beat St Mirren 2-1.
St Johnstone beat Kilmarnock 2-1 at Rugby Park. Francisco Sandaza gave the visitors the lead in the first half but Killie drew level through a Steven Anderson own goal. Cillian Sheridan then grabbed his third goal in two games to give St Johnstone the lead, rounding Bell and finishing with style.