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.
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Man of the match Barnes said afterwards: "It's tough.
"You score and it's an amazing feeling; you can feel the fans. We'd played really well. For 94 minutes, whatever it was, we were on top. To concede late on is really hard to take, but the score is level and we have a second leg to come.
"Absolutely. We kept the ball really well tonight and limited them with opportunities. It's going to be difficult, but tonight we showed what we can do. We were so close. The tie's still level and we believe (in reaching the quarterfinals)."