Rather than being triumphant, he chose the moment to get a few things off his chest - and he didn't miss his targets.
Immediately after any game, but particularly one with as much riding on it as Wednesday's, a manager can be vulnerable.
It's a like a release valve is opened, and all the pressure that has been building - in this case for a couple of months - comes pouring out.
You felt that was what you were witnessing as Neil had his say on the negativity surrounding the game here, the criticism of his players and the lack of help he believes he has had after bringing in over £50million in the past two years from qualification for the Champions League and the sale of players.
It's the last of these issues that might give most cause for concern and leave supporters wondering if there is a problem between Neil and the men who control the money at the club.
I honestly don't believe there is - otherwise, why would Neil have signed a new contract only last week?
I have always maintained Celtic's spending policy in this transfer window would be defined by whether or not they qualified for the group stage.
They were damned if they did, damned if they didn't. If they got there, they had got it right. If they failed, they had not.
Now, as yesterday's draw confirmed, they are back among the 32 clubs competing for Europe's top prize, so it must be acknowledged their strategy was the right one.
Understandably, Neil was unhappy about losing key players, Victor Wanyama, Gary Hooper and, most recently, Kelvin Wilson.
But he himself has admitted the money for Victor couldn't be refused, Gary wanted to test himself in the Barclays Premier League, and Kelvin felt he had to return to his family down south.
That brings it round to the replacements Neil has been allowed to bring in, and it was noticeable not one of the four - Amido Balde, Virgil van Dijk, Steven Mouyokolo or Derk Boerrigter - started on Wednesday against Shakhter
Like any manager, especially one trying to replace key men, Neil would have liked the opportunity to bring in even better players.
But the club have a transfer strategy which includes limits to what they are prepared to spend and the wages they are willing to pay.
Celtic simply can't go out and sign players who will guarantee them a place in the group stage.
You could see by the way the entire squad reacted when the third goal went in how united they are, and there is always a danger this harmony can be lost if you start to recruit players on bigger money.
What happens now that the Champions League place - and the money that comes with it - has been secured will be interesting.
Before they qualified, they were already in the process of signing Nir Biton from FC Ashod, and a fee had been agreed with Schalke for Teemu Pukki.
But I really don't see any huge shift in the strategy which has been followed up to this point.
That might further disappoint and frustrate Neil, but he has always known how the club is going to operate.
I am sure that, by the time he woke up yesterday, the anger he showed on Wednesday night would have been replaced by delight.
The guys who got stick for losing in Kazakhstan - which was unjust because they didn't play that badly in the first leg - really delivered when it mattered most.
It was the men on the pitch on Wednesday who really rose to the occasion, and it is those guys who deserve the credit for getting Celtic into the group stage.
Guys like Efe Ambrose, who had his best game in a Celtic jersey, and the scorers, Kris Commons, Georgios Samaras and James Forrest, got most praise.
But every single one of them played to their potential, which was exactly what was required to see off the threat from a Shakhter side who actually performed better than they did when they won in Astana.
The Kazakhs were cynical, but the Celtic players stood up to that and overcame it because they wanted the win so much.
Neil described it as his greatest achievement, and I would go along with that, given all the difficulties he and his side had to overcome in the qualifiers and play-offs.
He should savour the moment, take pride in what he has achieved with this group of players, and look forward to hearing that Champions League music at least another six times this season.