Moyes believes that his men could have kept possession more effectively to close out the match, but credited them for starting the match quickly and claiming a point in Ukraine.
He told Sky Sports News: "The team stood up well tonight, it was a good point against a side with a great home record. We got a good goal early doors.
"It looked like we would have stopped them from scoring until the goal. We said at half time we had to keep the ball better. I'm disappointed we didn't pass it better.
"If we got the second goal from Robin van Persie we would have seen it out."
United have now taken four points from their first two games in the competition under Moyes, establishing themselves at the top of Group A on goal difference.