After being pegged back twice, Barca were able to pull away in the second-half as they reached the quarterfinals 8-3 on aggregate.
Howe told ChronicleLive afterwards: "Our performance dropped - that was very clear. The first four goals you can't concede, two set-plays is unforgivable to a degree because you know how good they are in other aspects of their game.
"To concede two from regulation, from one free-kick and one corner, I can't be impressed. Psychologically, we did not recover from the penalty incident at half-time, for whatever reason that was, whether we felt we should have had a penalty at the other end, I don't know.
"There was certainly a dip in our performance. Our defending today was not at a level it was a few days ago. We were outstanding in many ways in the first half but we had too many individual errors."
Howe continued: "Yeah, it’s a tough way to go out. It’s really strange to try and sum that up, to be honest. I thought in the first half we were excellent—we went toe-to-toe with them, we created chances, and we looked a real threat.
"Albeit, we didn't defend the key moments well enough and there were a few individual errors that cost us.
"But in the second half, we were nowhere near as good as we were in the first. They’re a world-class side and they punished every single mistake. They deserved to go through on the balance of the two halves, but it feels incredibly harsh given how much we put into that opening period."
On Anthony Elanga's first-half double on the night, the manager added: "It was a great representation of how we play in that first period. We were brave, we pressed high, and we gave them a lot of problems. But at this level, if you slip—and we had two players slip for their first goal—you get punished. We have to learn from it."