The Hoops are only 1-0 up after the first leg of their Champions League second qualifying round tie, the crucial goal coming from 21-year-old Callum McGregor six minutes from time.
Manager Ronny Deila will analyse last night's match, then go over it with his players and backroom staff to point out what worked well, and what still requires attention. "My philosophy is every day to learn, and every day use to get better," explained the former schoolteacher. "We are going to do that this week, and we are going to perform even better when we get to Murrayfield."
With Celtic Park hosting the Commonwealth Games Opening Ceremony, it will be a step into the unknown for the Hoops as they play at the home of Scottish rugby.
But with their European season at stake - there is no parachute into the Europa League for losers at this stage - they know there can be no slip ups, or excuses.
Deila refused to press any panic buttons, despite just edging last night's tie, in which sub Thosteinn Ragnarrsson missed a golden chance to score for KR just a minute before Celtic broke the deadlock.
In fact, the Norwegian claimed he would have been happy with a draw in Reykjavik because his side made so many chances and delivered a performance which satisfied him.
Asked if he feared the goal might not come after seeing so many chances spurned, he replied: "The four matches we played before (in pre-season), we scored with every chance we had. In this game, we didn't score with every chance, but we created a lot.
"If it had been 0-0, I would have been happy as well because of the performance. But we deserved a goal, maybe a couple more."
Deila is confident his side is moving in the right direction, and that the style he wants his team to play is evolving.
He said: "In the second half, we were good at getting up the tempo going forward, and there was a lot of movement. When we lost the ball, we got it straight back again. That's how we want it."
The decision to play a friendly against Dynamo Dresden between the two legs of the tie against KR has raised a few eyebrows. But Deila says Saturday's game in Germany, and the friendlies on the following weekends against St Pauli and then Spurs are important building blocks in what he is trying to create.
He said of the Dresden match: "This is another opportunity to play a lot of players.
"I think it is important to play matches just now so that we can get to know each other and get things how we want them."
Deila was delighted his decision to give goal-hero McGregor his first competitive start paid dividends.
He said: "McGregor did well. I'm happy for him that he scored, and I'm happy with the defence, too."