Not long ago, questions loomed over Wilfried Nancy’s future as the manager of Celtic, with concerns about his tenure extending into the New Year.

After suffering four consecutive defeats, including a loss to St Mirren in the Premier Sports Cup final, the French manager appeared to be on shaky ground soon after his arrival.

The mood among many Celtic fans was one of skepticism, particularly following the team’s defeat against Dundee United on December 17, leaving them doubtful of Nancy’s capabilities.

However, a pair of victories in the span of a week has quieted some of the critics, at least for the time being.

There are signs of progress as the players gradually adapt to Nancy’s vision on the field. Nonetheless, the need for strategic player acquisitions in January is evident.

Benjamin Nygren celebrates with Kieran Tierney after putting Celtic back in front at Livingston

Wilfried Nancy watched his side edge closer to the top of table but there are still big concerns

Livingston celebrate their opener and had struck again before the clock reached eight minutes

If Nancy can navigate the transfer window successfully, he might still carve out a rewarding and enduring tenure in Glasgow.

First and foremost, he needs to address the glaring defensive issues which have plagued his side until this point. They shipped two in comical fashion within eight crazy minutes at Livingston at the weekend, and it could have been more had the hosts shown a little bit of composure in the second half.

Just like everyone else of late, Livi cut Celtic open far too easily and far too often.

That’s 13 goals conceded in six games. It simply isn’t sustainable.

Nancy’s insistence on playing a back three with two wing-backs isn’t going to change. And that’s absolutely fine. Let’s not forget, he has won trophies playing in this manner. But some of the personnel currently at his disposal aren’t up to it.

Anthony Ralston gets a lot of stick from the Celtic fans. Much of that is terribly unfair. But there’s no doubt whatsoever that playing on the right of this new-look backline doesn’t suit him. At no stage since Nancy’s arrival has he looked remotely comfortable in that position, and it was no different here.

Ralston has never lacked confidence in a Celtic shirt, but he looks so uncertain at the moment. His decision not to engage with Christian Montano as the Columbian raced through to fire Livi in front early on was baffling to say the least. He didn’t have a clue what to do.

Anthony Ralston looks completely out of his depth on the right of Nancy’s preferred back three

With Cameron Carter-Vickers out for the rest of the season and Liam Scales falling out of favour, a new centre-half is a must in the upcoming window.

A couple of wide men capable of playing the wing-back position wouldn’t go amiss either.

Yang Hyun-Jun is all over the place defensively, albeit that’s not necessarily his fault. It’s nothing to do with a lack of effort, but he is clearly still getting to grips with the position.

He left Montano completely free at the back post to smash home Livi’s second after moving inside in an attempt to give Ralston a hand dealing with Stevie May in the six-yard box.

It must be said, however, that he was much better going forward at the weekend, and was in the right place at the right time to net Celtic’s first equaliser, showing brilliant feet to leave a couple of defenders on their backside before finishing it off.

Needless to say, he’s far more effective in the opposition box than in his own.

Yang Hyun-jun struggled once again in a wing back role but did impress further up the park

It was the same story with regards to Luke McCowan on the other side. Livi boss David Martindale obviously targeted the 28-year-old as someone his side could get at, which they did.

It was a tough shift defensively for McCowan. But, much like Yang, he was a different proposition when on the front foot. Indeed, he was one of Celtic’s top performers in the final third.

Nancy may well believe that with time, both of them can be coached to learn the position, and that might be true. But Celtic will continue to be picked apart until then.

A new striker has to be fairly high on Nancy’s January wishlist too. Johnny Kenny isn’t the man to lead the line.

Having passed up several gilt-edged chances against Dundee United and Aberdeen in recent weeks, he was relatively anonymous here. His confidence looks shot to bits.

The problem is that Nancy doesn’t have many options to call upon if he wants to change things up. Kelechi Iheanacho has impressed since joining over the summer, but his injury problems are well-documented.

Johnny Kenny looks shorn of confidence up front and will surely face competition in January

The Nigerian isn’t much use to anyone if he can’t get on the park. And even then, he’s hardly got a reputation for being a prolific scorer.

A clinical No 9 would surely score a bucketload within Nancy’s attack-minded system, which is certainly entertaining to watch.

Some of the football on display in West Lothian — particularly during the first period — was outstanding. In all honesty, it’s night and day from what was often seen throughout Brendan Rodgers’ second spell in charge.

Benjamin Nygren was at the heart of it. For whatever reason, the Celtic punters have never really taken to the Swede since he joined the club from FC Nordsjaelland over the summer. Goodness knows why.

Granted, he has the tendency to drift in and out of games, but his numbers speak for themselves. He took his tally to 10 here in all competitions with a first-half double, the second of which being a sublime curling effort which found the top corner to put his side in front for the first time.

His manager is a long-time admirer of the midfielder, revealing afterwards that he previously tried to bring him to Columbus Crew, and is confident there is more to come.

It wasn’t an entirely comfortable day for Nancy but he was able to reflect on another victory

It’s still hard to pinpoint his exact position — he’s played in about six this season — but Nancy is getting the best out of him regardless.

Arne Engels is another who is growing in stature each week. It’s fair to say that the club’s record signing has failed to live up to expectations since making the move from FC Augsburg last year.

The Belgian even found himself out of the team at the start of the season, but Martin O’Neill appeared to give him a new lease of life, and his fine form has continued under Nancy. He looks much happier these days too.

Engels bossed the game on Saturday and slotted away Celtic’s fourth goal from the penalty spot with minimal fuss. He still needs to add more goals from open play to his armoury, but that will no doubt come with Nancy giving his midfielders license to get into the box at every opportunity.

Celtic aren’t out of the woods yet. But this team are now trending in the right direction, and that’s only going to continue once Nancy gets his own players in the building over the next month.