Arsenal were missing key players in Cesc Fabregas, Andrey Arshavin and Alex Song and, even though Marouane Chamakh came off the bench as they chased an equaliser, they failed to break a solid home defence.
"In the second half we came back into the game and gave a lot, you cannot fault the team, and we were a bit unlucky," added Wenger.
"We have learned the lesson that at this level you cannot lose focus at any moment and that is why we were punished.
"But we are still in a strong position in the group."
Wenger insisted he is not prioritising any one competition as Arsenal look to end their five-year trophy drought.
"At the moment we are not in a position where we can choose - we have to fight," stated Wenger.
"We have a difficult league game on Sunday against Newcastle. We will win what we can and not choose too much."
Shakhtar coach Mircea Lucescu praised his team for the way they came back from a goal down to register a win and extend their unbeaten home record to 49 games.
"It was a good match and an important win for me. I have been waiting for it a long time," he said.
"We should have stopped Walcott, but did not. However, I liked the reaction of my team, they played at a good level.
"Arsenal are a really good team, and we had to earn the points. The overall situation in the group did not clear up. Now we will just play the next games and try to earn more points."
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