What's interesting in the battle for position now is no longer Arsenal and Manchester City, but Liverpool and Manchester United because Newcastle managed to beat Brighton yesterday in round 25.
Mathematically, Newcastle have not passed the UCL because they still meet Leicester City, who are struggling to avoid relegation, and Chelsea, who could qualify for Man United or Liverpool.
Indeed, what you say is true, but on the other hand, looking at their current opponents, I think with Leicester and Chelsea it's not a big problem for them. Even if they can't win but if it's two draws from 2 games it's actually enough to get them in the Champions League next season and with Leicester in the state I think it's not even going to be a draw because their conditions are still very different and I feel Newcastle will won again against Leicester who are currently still slumped in the relegation zone.
On the other hand, against Chelsea, Newcastle still has a big chance, especially since they are still going through an update with their current new coach.