The Red Devils led at the break 2-0 courtesy of two goals from Danny Welbeck, but they had to rely on a late header from Ashley Young to secure a share of the spoils after their Swiss opponents hit back with three goals in the second half.
"3-3 after being 2 nil up isn't what we wanted, we'll do better Saturday," the central defender said on Twitter. "Pleased for Welbeck getting a brace. We have to go to Basel + win."
The draw has left United with two points from as many European matches this season.