Welbeck scored to have Brighton 2-1 ahead before Forest's found an equaliser via Ramon Sosa. Forest boss Nuno and Brighton counterpart Fabian Hurzeler both saw red after Morgan Gibbs-White was sent off for a tackle on Seagulls striker Joao Pedro.
Welbeck later said, "Considering the position we were in today, 2-1 up, the feeling is disappointment. It is really hard to take.
"It is a harsh lesson for us but it is one we have to analyse and work through on the training pitch and make sure if we are in this position again it doesn't happen again.
"The game has ended in a draw again today when we really should have closed it out so it is really frustrating. A lot of disappointment in the dressing room and in the whole club, fans included."
On his goal, he said: "I've had a couple of close ones recently and it fell nicely for me. It was in a spot where I fancied my chance and it was a good free kick, one that I am happy with. We move on to the next one now.
"We have got a great culture in the dressing room where everyone wants to improve and elevate the levels. We csn take the positivity of being unbeaten but take the disappointment of today and last week to fuel us to get better. There are moments where we have been naive but we can look back on that and improve."