Danny Welbeck's 18th-minute opener paved the way for United to become the first English team to win at the notoriously intimidating Donbass Arena, only for Taison to level 14 minutes from time.
United managed just one shot on target during the game, and Moyes feels a more fluid passing game could have seen his team record a second Champions League win of the season but was happy with the overall display.
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"We said at half-time we needed to keep the ball better, but we actually gave it away more in the second half, so I was disappointed we didn't pass it better.
"We carved out a really good chance and Robin [van Persie] was a bit unlucky not to get a second goal and I think if we'd got that we would have seen it out quite easily.
"I think their goal goes through Michael Carrick's legs and then goes through one of their players' legs before it reaches Vida [Nemanja Vidic] and they get a ricochet which gets them the goal, so we were really unlucky to lose a goal.
"Although it is a point in the Champions League, it doesn't take us any further just now. We're going to have to win other games if we want to progress in the competition.
"On paper this looked a hard away tie and we have picked up a good point."
Moyes also hailed Ryan Giggs, who became the most-capped player in Champions League history with his 145th appearance when he replaced Marouane Fellaini in the second half.
He added: "It was fantastic. I was telling him before the game he was going to be subbed on, he was going to come on off the bench. What a record, and I've got to say, what a player."