The Magpies entered the game knowing they needed a win to have any chance of progression into the knockout stages.
And Joelinton lifted the roof off St James’ Park with a stunning 33rd-minute strike past Mike Maignan.
Borussia Dortmund then took the lead against PSG in Germany, leaving Newcastle comfortably in second in Group F.
However, PSG equalised moments later, and on the hour-mark, Christian Pulisic equalised for Milan on Tyneside, dropping Newcastle back down to third.
Howe’s side hunted for a winner, but Samuel Chukwueze spiked a dagger through Geordie hearts with a late go-ahead goal shortly after entering the pitch.
It left Newcastle bottom of Group F, meaning even the consolation of Europa League football evaded them in the dying embers of the campaign.
Newcastle wouldn’t have been in as much of a perilous position had they held onto their 1-0 lead at PSG on matchday five.
Howe’s men were seconds away from a momentous victory in Paris before a controversial VAR decision penalised Tino Livramento for handball. Kylian Mbappe converted the spot-kick to earn a point.
PSG’s draw at Dortmund on Wednesday earned the Ligue 1 champions a spot in the last 16 over Newcastle and Milan.
However, Howe refused to blame his side’s late heartbreak at the Parc des Princes and insisted it didn’t play on their minds in the curtain-closer.
“I think it would be foolish of me to look back and start bringing up old stuff,” Howe told TNT Sports.
“We had the opportunity tonight to do what we had to do, and we didn’t take it. We couldn’t have tried harder. I don’t think we left anything on the pitch.”
Newcastle faced a tough enough test in the Champions League’s group of death and have been heavily hampered by relentless injury issues in recent weeks.
And while Howe turned focus away from the controversy in Paris, the English coach did bemoan his availability issues.
He added: “[We’ve learned] so much. The value of the squad, first and foremost, is what has exposed us.
“The fact we haven’t had the ability to utilise the squad we’ve created… We’ve gone into games very limited in what we can do, and that hasn’t helped us.”