The Magpies came into the game knowing they had to win, and dominated for long spells, but were undone again by their own shortcomings at the back.
Titus Bramble has been in impressive form of late, but he had one of those moments he will want to forget as he was caught in possession inside his own box and Patrick Kluivert nipped in to poke the ball past Shay Given.
Thiago Motta was allowed the freedom of St James` Park to flick home the second from a free-kick on 75 minutes.
Craig Bellamy was the main source of Newcastle`s attacking play and he had three good chances in the first-half, but the closest he came to scoring was when his shot following great play by Kieron Dyer and Alan Shearer hit the post.
Laurent Robert had a fizzing free-kick that went wide and Bramble saw his effort from a corner cleared off the line.
Barca were prepared to play on the break and it was a hopeful ball over the top that brought the killer first goal.
Kluivert chased more in hope than expectation, but was handed a real present when Bramble decided not to clear the ball and he stuck out a foot and prodded the ball past Given to silence St James` Park
Newcastle rallied, with Bellamy, Dyer and Hugo Viana going close, but they were unable to find a way past Victor Valdes and Motta`s late goal taught The Magpies another lesson about European football.
As it turned out, a win would not have been enough for Newcastle as Internazionale went to Bayer Leverkusen and came away with the three points.
Bayer gave it a real go, but were undone by a defensive error of their own as rookie forward Obafemi Martins burst clear before shooting low past Hans-Jorg Butt.
Butt saved a penalty from Domenico Morfeo, and the Germans threw everything at Inter after the break, but the Italians held firm and snatched a late second from Emre Belozoglu to reach the last eight.
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