Many Celtic supporters are feeling sore, and with good reason, because a combination of failings has left the club bereft and floundering in the Champions League this season.

Tuesday night's 0-3 humbling at home to AC Milan perfectly captured where Celtic have failed, on and off the pitch. It left Neil Lennon to explain away what to many might have seemed pretty obvious.

Last summer Celtic raked in close to £20m in transfer fees through the sales of Victor Wanyama, Gary Hooper and Kelvin Wilson. The club's response in replacing two of those players proved either inadequate or actually impotent.

Finding a new, accomplished striker became particularly galling. Lennon would have loved Kevin Doyle to come to Celtic Park, but the Wolves striker's wages after two years in the Barclays Premier League were beyond the SPFL club.

With Hooper gone, and with Doyle unreachable, you got the impression Celtic were left spreading their transfer honey pretty wide and thin. In truth, it ended up being a mess.

Amido Balde arrived for £2m. Derk Boerrigter came for something similar. On the last day of the August transfer window in came the little-known Teemu Pukki for £3m in what looked then and now like a last-gasp clutching at straws.

That amounted to around £7m being spent, but on what? Every striker Celtic bought last summer came with a large question-mark attached. They proved to be expensive risks.

I'm minded here of an incident involving Walter Smith, and a decision he made in what proved to be his last season as Rangers manager in 2010.

Smith was surprised that summer to be told he had £5m to spend for reinvestment in his Rangers team. Most believed that two, maybe three players in the £1.5m-£2m range would be signed up.

But Smith thought long and hard about it and decided to invest close to the whole sum - £4m in fact - on one player. He surprised many but went with his conviction. He bought Nikica Jelavic from Rapid Vienna and in one fell swoop landed a striker of genuine quality.

It is what Celtic did not do in the summer. They spent cautiously and ended up with a watery quality. On Tuesday night against Milan Neil Lennon had three strikers from which to choose - Balde, Pukki and Anthony Stokes - but felt confident with none of them and went with Georgios Samaras instead.

On top of this, Lennon was let down by certain players on the park; in particular two of them who are, ironically, among his best.

Scott Brown's stupidity in kicking out at Barcelona's Neymar in October meant he was posted missing for three subsequent group games. Brown is no world beater but on these occasions his team badly needs his drive and energy.

On top of that, the giant Fraser Forster, for all his qualities, simply refuses to command his six-yard box when under aerial threat. When Kaka headed Milan ahead after 12 minutes, the Brazilian was five yards from Forster's goalline yet the goalkeeper was still loath to come and challenge for the ball.

It remains a glaring omission in Forster's armoury, and it immediately cost Celtic and put them on the back foot against Milan.

Up in the stands, Celtic had other worries to contend with, notably the antics of the Green Brigade, who are now pushing Celtic to the extremes of embarrassment and likely trouble.

The Green Brigade have a faction who are determined to score public points about Irish Republicanism and the IRA.

Anyone who delves into these football club/political narratives, on display all over Europe, knows how complicated they are. But one aspect is not complicated at all - trouble brews for Celtic whenever this group of supporters goes down this road.

On Tuesday the Green Brigade displayed further words and images that will have made Peter Lawwell, the Celtic CEO, squirm in his seat.

The vast majority of Celtic supporters have no time for this political polemic at all, but the Green Brigade couldn't care about that. Instead, they persist with these displays, and will crucify Celtic in the eyes of the authorities, unless someone can persuade them to relent.

* In the hours following this column being filed, Uefa announced it was opening disciplinary proceedings against Celtic FC over "illicit" banners displayed by fans at the Champions League game against AC Milan.