"Our disappointment today is the two goals conceded," the Arsenal manager told reporters.
"We are speaking before each match to take a mentality of 'don't concede chances easily'... but the last 30 minutes, we needed to be better on this competitive aspect.
"We need to continue to improve on this because in the last minute in Newcastle and again today in the last 20 minutes, we conceded two goals. Our challenge is to be competitive for 90 minutes of each match and this is one thing to improve."
The two Vorskla goals spoiled an otherwise assured display on debut from German goalkeeper Bernd Leno, while Swiss full back Stephan Lichtsteiner and Lucas Torreira also made their first Arsenal starts.
Emery remains hopeful Torreira will feature against Everton in the league on Sunday after the Uruguayan midfielder picked up a knock on his knee in the second half.
"Each minute he is playing, he is doing very well," he added.
"I hope that tomorrow and Saturday, he will be okay for Sunday.
"And for Leno... I think that we conceded two goals but not for a mistake. For him, it takes minutes for the game and confidence for continuing also because he will be continuing to play matches in the next week."
