Welbeck put United in front in their UEFA Champions League Group A clash against Shakhtar Donetsk at the Donbass Arena before Taison levelled for the hosts 14 minutes from time.
Moyes has come under fire following a miserable start to their Premier League title defence, with Saturday's 2-1 home defeat by West Brom a significant low.
But there were far more positives to take from a disciplined display in Ukraine, against a side who have never lost a Champions League game at home to English opposition.
Welbeck told Sky Sports: "In the end it was a decent result. We went ahead when we got the goal early on and we made ourselves hard to beat, it was really difficult for them to score. Towards the end they got that goal and that's the disappointing part.
"I don't think many teams have come here and got three points. We would have liked to get three points but it wasn't to be.
"I think four points from the first two games is alright, especially coming away to Shakhtar and getting a draw. Obviously, we're Manchester United and we want to win every game, but coming here and getting a point, we have to be satisfied.
"Things aren't going as well as we would have liked in the Premier League, but what we've got to do is gather together and concentrate on our next game and not look too far into the future."