The Ukrainian side scored three second-half goals at the L'viv Arena on Tuesday in a comprehensive and much-needed Group A win.
Olexandr Gladkiy opened the scoring in the first half before a Darijo Srna penalty and efforts from Eduardo and Alex Teixeira saw the hosts to their victory, as Kari Arnason was sent off in stoppage time.
Having beaten Shakhtar on matchday three, Hareide said his team simply failed to execute away from home.
"We had a similar plan but we were not aggressive enough and gave Shakhtar too much space," he said via UEFA.com.
"Shakhtar raised the tempo and played much better than us. We couldn't get close enough to them so they kept the ball and made us commit mistakes.
"You have to always be at your top level in the Champions League. We can promise we will try 100 per cent in our matches against Madrid and Paris."
With their first points in the group, Shakhtar moved up to third – but they are well behind Real Madrid (10 points) and PSG (seven).