It will be a massive hill to climb now for the Geordies, to try and ensure their season isn't over yet.
Newcastle were outclassed by the Gunners, their poor defensive showing was made a mockery of by Bergkamp and co.
Even without Thierry Henry, Arsenal were still miles better than a Newcastle team without key players Speed and Bellamy.
Arsenal took the lead on 61 seconds, Bergkamp teeing up Robert Pires to strike a perfect shot into the bottom left hand corner, past Shay Given.
Bergkamp needed only another eight minutes to double the scoreline himself, sidefooting home a Wiltord cross.
Distin and O'Brien both had decent chances to get their team back into the tie, but both were wasted.
Alan Shearer came close when he tried to chip Richard Wright, and Wright had trouble dealing with a Laurent Robert free-kick.
Given had to make two crucial saves from Wiltord and Ljungberg just before half time, to keep Newcastle's hopes alive.
Newcastle came out strongly in the second half, but their FA Cup dreams were soon dashed when Arsenal scored again.
Luzhny won a free kick at the edge of the box, and Bergkamp's cross was met with a strong header by Sol Campbell.
Bergkamp went on to torment the Newcastle back-four even more, as he narrowly missed with a clever chip, and then shot just wide minutes later.
Carl Cort put a strong header wide, but then made amends with his next attempt, only to see his goal dissallowed for offside.
Newcastle had several bright periods, and had several good chances to keep themselves in the Cup, however, they are at risk of allowing their season to freefall into oblivion.
The return of Speed and Bellamy will make a big difference to team morale, but the last month has shown the lack of depth in the team.
Te results have meant that no longer are Newcastle challenging for the title, they are out of the cup, and are in danger of allowing Chelsea and Leeds to overtake them in the race for Europe.