United are third in Group A, behind Fenerbahce and Feyenoord, following a tight victory for Jose Mourinho's men, with captain Wayne Rooney again left on the bench.
Ibrahimovic scored for his seventh different club in European competition, but the veteran striker thinks United found it difficult to create space against a determined Ukrainian outfit.
"It was not an easy game," Ibrahimovic told BT Sport. "We played good and created some chances but it was a difficult game.
"If you don't score early the spaces get smaller and you have to find a way to score. After the goal, we had more space but it was a decent game. We won and that is what counts after losing against Feyenoord [on matchday one].
"If you want to go through you need to win the game and we won. We could do much more, I expect more from the team but we are playing well.
"We had a good game, we won, and it’s good for confidence. We need to step it up and do a lot more."
Ibrahimovic played down his role in United's goal, which came from their first shot on target, with substitute Rooney's mishit effort ballooning up for his close-range header.
"We play as a team," the Swede said. "We create as a team. We are trying. Sometimes we create a lot and sometimes we create less.
"The important thing is to create chances and be focused for when the chance came - and when it came it went in."
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