It is only 12 months ago that they were a side who were teetering on the edge as they drew 3-3 at Rugby Park with Kilmarnock.
When you consider just how far they have come in such a short space of time, it is quite remarkable.
Everyone deserves credit for the victory they recorded in Russia this week – the players, the management staff, the backroom team and the small band of supporters who made the journey.
I thought the manager got the team selection spot on. He got the shape and the balance right and he made his substitutions at the right time to have maximum impact.
One of the things that really stood out for me and that hasn't often been mentioned, is just how fit this Celtic team is.
To go away from home in the Champions League, the most demanding environment of all, and be able still to be hitting on the counter-attack in the final minute of the match shows just how physically capable Celtic are at this level.
There is, rightly, a real sense of confidence and what I would call accepted arrogance now about Celtic.
It is an arrogance that many top teams develop and it comes simply by winning games and getting results.
I don't think they will be getting too far ahead of themselves in the Champions League because they have a double-header against Barcelona looming, but I do think that they will go into these contests with a great deal of belief.
It would also appear, judging by the game last weekend at Fir Park, that the Champions League is not a distraction for Celtic.
It can always be a test to come back to a domestic game after playing in Europe, but Celtic can now count to a very fit and durable squad.
Lennon will be able to tweak things and bring others in without it unsettling the team too much.
Guys like Beram Kayal and Joe Ledley are waiting to get back in and, due to the way that the team are playing at the minute, no-one will want to be out of the line-up for fear of losing their place.
For the game against Hearts on Sunday I am sure that Lennon will change things slightly, but I think given just how efficient Celtic were at Fir Park, the signs are there that this is a team who have their tails up and who are ready to keep the momentum going.
Over the summer, Lennon was sensible in the transfer market. He was able to reduce the quantity but increase the quality and I think that has shown in the performances produced so far this season, especially in Europe.
Kelvin Wilson is looking like a different player and his fledging partnership with Efe Ambrose looks like it could be a good one.
If you were nitpicking you would feel that Wilson may have done better with Spartak's equalising goal in Moscow the other night and also that Fraser Forster may have done better with the second, but these were minor incidents that shouldn't detract from the overall performance.
I can guarantee that both players, who have played very well in recent weeks, will have taken a lesson from it, but like I say, it is nitpicking from a night where there was so many positives for Lennon to take.
As for the manager himself, he is right to enjoy the plaudits that come with such a good result.
He got the team selection absolutely right and the big thing now will be the belief and the confidence that comes with such a result.
Ironically, I hadn't realised that I actually oversaw the last away win in the European Cup prior to Tuesday night's victory – and that was an away win over Shamrock Rovers.
The Champions League is the biggest stage of all for club football and finally getting that away win in the competition will be a monkey off their backs.