Lack of clinical edge
The Hoops had plenty of chances, particularly in the first 45 minutes.
Kyogo Furuhashi had a header that was saved by RB Leipzig's goalkeeper, and then, only moments later, he had a shot deflected wide.
Jota did score in the second half, but overall, Ange Postecoglou will be disappointed they did not find the net on another occasion earlier on.
If one of those chances had been converted, it could have been a different game.
It is a problem that plagued the team against Shakhtar, which continued during matchday three of the group stages.
Defensive fragility
The Scottish champions really struggled at the back. It was a night where the back four were unable to deal with the waves of opposition attacks.
Several times the ball was played in behind, and the Parkhead defenders were nowhere to be seen.
There seemed to be a real lack of concentration at times, and this was clearly highlighted when Joe Hart made a major error of passing the ball right to Andre Silva, who dispatched the finish past him to put the Germans 2-1 up.
As well as the goals conceded in the 3-1 defeat, there were two tight VAR calls for goals that ended up flagged offside.
Postecoglou will also be frustrated with how many times the defence gave the ball away.
McGregor injury blow
The captain going off early on in the match made it an uphill struggle for the Hoops.
He pulled up not long after Marco Rose's side went 1-0.
Celtic losing his influence in the middle of the park no doubt played a part in the defeat.
Oliver Abildgaard replaced him, but it is clear the Dane is not at full-match fitness.
Not having the Scotland international to progress the ball quickly meant Postecoglou's men could not build properly from the back.
This meant there was a lack of legs in the middle of the park, and Leipzig could regularly cut through the Hoops' midfield.
