The results have been accompanied by a backdrop of constant questioning of Celtic's transfer policy. Barely a press conference goes by without Brendan Rodgers being asked about progression on potential signings or his general thoughts on the club's recruitment.
He has declined to answer some questions on the issue and more recently dropped the bombshell that he would quit if he felt that the club's ambitions did not match his.
The last week has only increased the brightness of the spotlight on Celtic's activity, or lack of, in the transfer window.
Even with the defeat to Hearts, and the feeling that Rangers are beginning to get their act together, there is no doubt that Celtic still have the players to ease to a Ladbrokes Premiership win, and perhaps another domestic treble. But for someone as ambitious as Rodgers that can't be enough. He will want to leave his mark on European competition.
So in what areas do Celtic need to strengthen?
With two Scotland goalkeepers in Craig Gordon and Scott Bain, Celtic are well stocked in the goalkeeping department, especially as their No.1 is the best in the country.
Mikael Lustig surprised many by helping Sweden reach the quarter-final of the World Cup during the summer. It was on the back of a decent rather than great season for the 31-year-old.
Since joining at the start of 2012, Lustig has been a fine servant for the club. Not only has he performed excellently on the pitch but he bought into the club as a whole quickly, endearing himself to fans with playful antics and playing as if he was a lifelong fan of the club.
But there is no doubt his capability as a right-back has waned. He has arguably performed better when tucked in as a right-sided centre-back. And there were some who would have kept Cristian Gamboa in the team following the Costa Rican's performances against Rosenborg.
It is a position that certainly can be improved upon, however the priority depends on Rodgers' formation preference. If he sees a back three as the system going forward with James Forrest as a wing-back then there are more pressing issues.
It's the position which has attracted most attention. Not just this summer but going back to Rodgers' first transfer window when it appeared that Jozo Simunovic would depart, only for the Bosnian to become a key figure in the club's unbeaten domestic season.
A team with five centre-backs on their books should not require a sixth, let alone a team who have thoroughly dominated domestically in the past 24 months. That would be the case if those centre-backs were consistently available. That hasn't been the case for Simunovic and Compper, with the former showing a great deal of inconsistency over the last 12 months.
Meanwhile Dedryck Boyata has reportedly downed tools as he looks to force a move away from the club with only one year left on his contract. It has left Celtic stretched with starring centre-back Kristoffer Ajer unavailable for Celtic's crucial second-leg clash with AEK Athens in the Greek capital.
Obviously too late to rectify ahead of the Champions League encounter, a new centre-back should now be regarded as a priority. Ajer is a certain starter but Jack Hendry is still improving. The former Dundee centre-back has not yet played 75 first-team games despite being 23. Contrast that with Hearts' John Souttar who is two years Hendry's junior but has played nearly 160 games.
It becomes even more pressing if Rodgers opts for three centre-backs as his preferred defensive base.
Celtic have one of the best young left-backs in the world and two able deputies.
The John McGinn saga only increased the disgruntlement felt by fans towards Celtic's recruitment drive. The champions appeared to be in the driving seat for Hibs' talisman before Aston Villa swooped for the player. A couple of hours after Celtic's defeat at Tynecastle Park, McGinn provided two assists to help Villa to a 3-2 win.
There is no doubt Celtic have a lot of talent in the centre of the pitch but having lost Stuart Armstrong they are lacking a dynamic and direct option who can break through the lines with driving runs, with and without the ball, from deeper positions.
Scott Brown, Olivier Ntcham, Callum McGregor and Tom Rogic are Celtic's main midfield options but McGinn would have made that fearsome quartet a fearsome quintet. On more than one occasion Armstrong proved his worth off the bench, helping turn games in Celtic's favour or by simply keeping up Celtic's domination.
McGinn was an affordable successor. Now Celtic will be hard pressed to find someone who can do similar and slot into the midfield.
Celtic have been heavily linked with a loan move for Daniel Arzani from Manchester City, plus another move for Patrick Roberts who spent the last two-and-a-half seasons on loan at Celtic Park.
Yet, with the likes of Lewis Morgan, Jonny Hayes, Ryan Christie, Mikey Johnston, not to forget James Forrest, Scott Sinclair and Callum McGregor, it is surprising, on paper, if another option or two in the wide areas is required.
It becomes more understandable following Saturday's defeat where Hayes struggled to make an impact and Sinclair continued his poor form. The latter has transformed from arguably the best player in the league and a match-winner to someone who appears to be going through the motions, cutting in from the left and being crowded out on a weekly basis.
Morgan and Johnston are two talented youngsters for the future.
Domestically, it is more than enough but for the European stage it is understandable if Rodgers is in need of more match-winning quality.
Moussa Dembele, Odsonne Edouard and Leigh Griffiths. All capable of hitting 20-plus goals.
There are two key areas which require strengthening: A centre-back capable of coming in and complementing Kristoffer Ajer and a dynamic midfielder as a replacement for Stuart Armstrong.
If the correct options present themselves, a right-back and attacking wide player would be fine additions to the Celtic squad.
The worry is that the club may have left it too late in terms of helping the team achieve Champions League group stage qualification for the third year running.