The Toon were always in control for the 3-2 victory, which saw them win their playoff tie 9-3 on aggregate.
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Howe said afterwards: "It's a massive achievement from us to get to the last 16. I've loved the new format, I think it's a really good thing. I've really enjoyed it.
"Coming to the pressure games, the double-headers, we've navigated that really well. I don't think it was a great performance, but I'm really pleased that we won."
The result now will see Newcastle meet either Barcelona or Chelsea in the next round.
Howe added, "Whoever we get in the next round will be an amazing tie for us. It's a massive thing for us, to give our season an extra boost to get through this play-off and onto the next one."