"It is a tough place to come as they have a good team and some good players," UEFA.com quotes him as saying. "We knew it was going to be difficult but we went 1-0 up and we had a good start.
"But then they began to push forward and had possession. I don't think they created a lot of chances yet they managed to score a goal.
"In the end I don't think we should be unhappy with our performance, if we look at the games we played over the last few weeks."
Vidic added that United can take heart from their display in Donetsk and improve their performances in the Premier League.
"It is not just us who have started badly in the Premier League," said the centre-back. "If you look at the other teams who compete for the title, they haven't had great starts either.
"I think we will have some tough matches this season. I don't think we played as we can today, but from this match there was some improvement and hopefully we can improve our form and get a few more wins."
United are currently 12th in the Premier League table with seven points from six matches.