Barkley had Villa ahead before Evanilson struck an injury-time equaliser for the visitors.
The midfielder later said: "Disappointing really. After we got the goal I think we could have played out better and we went long a lot. The late goal, we work on our defensive side and it is really disappointing to concede that.
"It was nice for me to finally get that (first goal) in front of the fans but overall it is disappointing really.
On manager Unai Emery, he added: "Working with him every day since I have been here, I can see the growth of the club. We are fighting to remain in the Champions League.
"We are growing and learning every day and the manager is pushing us as far as he can./ Today we can hopefully take lessons from because we have to fight until the end. It's like two points lost, really."