The striker had put United ahead on 19 minutes with a predatory strike from inside the area, but the hosts clawed back an equaliser through Taison deep into the second half.
Shakhtar have never lost to an English side on home soil in Europe's elite club competition, and Welbeck was happy with the result that puts the Reds on top of Group A.
"In the end it was a decent result, we got the goal and went ahead early, and made ourselves hard to beat," Danny told Sky Sports. "It was really difficult for them to score but towards the end they got that goal, and that’s the disappointing part.
"Not many teams come here and win, we would have liked to got all three points but it wasn’t to be. Just now we’re looking to the next result and that’s the most important thing.
"Four points from the first two games is alright, especially considering we have come away to Shakhtar and got a draw," the 22-year-old added.
"We’re a bit disappointed, we’re Manchester United and we want to win every game so getting a point here, we’ve got to be satisfied with it."