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.
Afterwards, Howe said: "I'm just devastated we could not get the win we deserved. That's football, it never plays to romance.
"There was so much good about our performance tonight, so much of us at our best. It was a great advert for us as a club on and off the pitch. We did our bit and the crowd did not let us down, they never do.
"So the last kick of the game, that is a tough one to take. If you switch off for a second, they will punish you. We had done so well defensively all night."
Howe continued: "The tie is very much alive. We've been competitive and shown we can play against the very best when we're at our best.
"In the cold light of day when we wake up, we'll see the positives. The tie is very much alive, we played really well.
"We showed our qualities. We've been really competitive. The challenge is we need more on a consistent basis. We've showed we can play against the very best when we're at our best."
Asked if he felt Newcastle deserved more, Howe said: "Yes, we do. A really good performance from the team, very, very good in all phases, really. I thought we limited them with a really good defensive performance from the team and I thought we attacked really well too.
"Although we didn't create an abundance of clear-cut chances, I thought there were chances all through the game for us.
"It was great to see us finally score and then the last attack of the game, the last kick of the game, it's a tough one to take."