United were beaten 1-0 at Kingston Park thanks to an 89th-minute winner from Durham Women's Mollie Lambert.
That came after Becky Langley's side created numerous goalscoring opportunities throughout the match, but were unable to find a way past Tatiana Saunders.
However Stobbs remained level-headed despite the tough loss, with United having achieved back-to-back promotions to reach the second tier of women's football.
"We're gutted with the result," Stobbs admitted post-match. "I think we've now got to pause and reflect on what went wrong.
"When games like that happen and you create loads of chances, we've got to put them away because at this level, you get punished.
"You learn the most from these sorts of matches and we're only five games into our season.
"If you look at our journey over the years we're still in a good place, but we've got to learn from today and pick each other up.
"Everyone is down in the changing room but we win as a team and lose as a team and I know we'll bounce back."
Despite being the more dominant side over the course of the match, United struggled to find a cutting edge in the final third, allowing the away side to steal all three points.
While it was a first league defeat of the season, it was also a North East derby loss which stings all the more, and skipper Stobbs knows she now has a big role to play off the pitch.
"I think we controlled the game but it was those key moments, whether that be the final pass or backing ourselves when we get into the final third a little bit more," she added.
"We've got to be more clinical on the ball as a whole team because this is a ruthless game. We'll take this loss as a lesson, learn from it and move forward into our next match.
"I feel like my job as captain is to ensure the group remains positive, pick people up, because this is football and we've just got to learn from it."