Harvey Barnes gave Newcastle an 86th minute lead in the first-leg of Tuesday's round of 16 clash before Lamine Yamal converted a 96th minute penalty won by Dani Olmo.
Hall said afterwards, "I thought we were outstanding today, and the last goal doesn't reflect our performance really.
"If we're taking the game to them at 1-0 for the second leg, we're in a really good position.
"We can be really proud of the effort we put in today. They're obviously a top side, and we knew the game was going to be difficult, but, as I said, we can be so proud of ourselves.
"Whenever we play here, we want to start sharp. Anyone who plays against us knows that's what we want to do, and I thought we did it really well today. I felt our energy levels and fitness levels carried on throughout the whole 90 minutes. Like I said, I think we deserved more from the game, really.
"Whenever we're on a high, we want to keep going, we want to keep pushing. And that shows a lot about our mentality. Sometimes in these moments, it's easy to get carried away. And I guess there's an argument that maybe we did at the end there, trying to push for another goal."
On going to Barca for the second-leg, Hall added: “Obviously, it's going to be tough to go there and get a result, but I feel like with our team, our squad – if anyone can, we could do it."