The Hoops dominated for the vast majority of the game in the Legia Warsaw municipal stadium but had to settle for a 1-1 draw.
The Scottish champions had several chances even before Artem Bondarenko put through his own net in the 10th minute following a penetrating run from Reo Hatate.
Shakhtar equalised out of the blue in the 29th minute after a pass inside Josip Juranovic gave left-winger Mykhaylo Mudryk a clear run at goal.
Former Celtic winger Marian Shved had a goal disallowed for offside and forced a good stop from Joe Hart as Shakhtar enjoyed a bounce until half-time.
But Postecoglou’s side regained control immediately after the interval and substitutes Giorgos Giakoumakis and Daizen Maeda missed the best of a series of opportunities.
“The performance was excellent,” the Celtic manager said.
“Obviously the result was not reflective of that but I thought in the whole game the players gave everything and that’s all I can ask for.
“We needed that second goal and we had good chances to get it. From my perspective I can’t ask for more from them.
“We will get our rewards if we keep playing that kind of football and showing that sort of commitment.”
Celtic also missed chances during their 3-0 opening defeat to Real Madrid but Postecoglou was more upbeat this week.
“I think more significant than the point is the performance,” he said.
“It is the highest level of club football, every game is pressurised, every moment of every game is important. I just thought there was real growth in our team and in the way we handled it all.
“You definitely have to earn everything at this level. Every point and every win will take maximum effort from us and for us to be at our best.
“It wasn’t three points but in terms of the performance I thought that was the most encouraging part. The players really embraced the fact we will have to be at our best all the time for everything we get.”
Celtic had 16 attempts at goal compared to Shakhtar’s five.
Postecoglou said: “Last week we were good for 55, 60 minutes and then the opposition sort of got on top of us.
“Here you are away from home and obviously it’s a neutral venue but it’s not your home ground and I just thought that they showed resilience and mental toughness to keep playing our football. At this level I think that is encouraging.
“We put everything into it. We didn’t get the three points but if we keep doing that I think it will give us a chance of being successful in every game we play.”
Shakhtar manager Igor Jovicevic expressed pride in his players for claiming a point.
He added: “They are super fast and a super aggressive team and we knew exactly what we were about to face. The pressing, especially in the beginning, was incredible.
“The game was a very good experience. Yes they gave us a very hard time but don’t forget we were supported by 40 million fans in Ukraine and we claimed a point and scored a goal.
“This game is something to be really proud about. We turned the impossible into possible, we turned the improbable into probable.”