NEWCASTLE -- The Champions League can be as brutal as it can be glorious, and Newcastle United have learned the hard way that club football's biggest competition can never be taken for granted.

In the space of 90 minutes against AC Milan at St James' Park on Wednesday, Eddie Howe's team found themselves on course for the Champions League knockout stages, then preparing for the consolation prize of a place in the Europa League, before ending up with nothing at all after two second-half goals sealed a Milan fightback to inflict a 2-1 defeat on the Magpies that left them bottom of Group F.

Just like Manchester United 24 hours earlier, Newcastle were eliminated from the Champions League and out of Europe altogether after recording just one win in the competition. Two of the wealthiest clubs from the richest league in the world and all they could manage was the humiliation of a pre-Christmas exit from Europe.

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Rewind to that incredible night in early October, when Newcastle marked their first Champions League home game for 20 years with a stunning 4-1 win against Paris Saint-Germain, and it seemed that the raucous atmosphere at St James's would carry Howe's team all the way into the Round of 16.

But after completing their group campaign, that victory against PSG turned out to be Newcastle's only win. Home defeats against Borussia Dortmund and Milan brought them crashing down to earth and out of the competition.

The general rule in the Champions League is that teams will qualify from a group if they win their home games and pick up a point or two on the road. There are exceptions of course, but losing twice on home turf is always a recipe for an elimination, especially if you can't find an away win.

Newcastle might complain about fine margins denying them a top two finish. They were harshly done to when conceding a stoppage-time penalty against PSG in Paris last month after a dubious handball decision against Tino Livramento, and Milan goalkeeper Mike Maignan made a world-class save to keep out a Bruno Guimarães shot in the closing stages when the score was still 1-1.

But Milan also struck the post twice in this game through Rafael Leão and Fikayo Tomori and the Rossoneri ultimately deserved their win thanks to goals from Christian Pulisic and Samuel Chukwueze, who ultimately rendered Joelinton's first-half opener meaningless.

"The save at 1-1, how close it is to going in, they are small margins," Howe said in his post-match press conference. "I don't think we have been outplayed in any game -- the Dortmund game could have been different, but that's the elite element of the game at this level.

"I feel for the players. I have seen what they've given. We weren't at our absolute best tonight. It's painful for me and them because I know how much they have put in.

"We have gone into Champions League games without key players due to injuries and that has hurt us."

Those injuries have accounted for a full team of players at one stage and Howe was unable to fill the substitutes' bench against Milan. Key absentees included the injured goalkeeper Nick Pope, defender Sven Botman and forward Harvey Barnes, while Sandro Tonali, the summer signing from Milan, started a 10-month suspension for breaching betting regulations in October.

As a consequence of many unavailable players, it is difficult to convincingly suggest that Newcastle's return to the Champions League this season has been a write-off.

It has certainly been a learning process, with two defeats against Dortmund offering an example of how teams just below the absolute elite can pick you off with smart tactics and experience of playing in this competition. And Howe and his players might reflect on the 0-0 stalemate in their opening game in Milan, when a safety-first approach in the San Siro earned a draw when the reality was that the home side were there for the taking had Newcastle been more ambitious.

The win against PSG was a night when it all came together, and Newcastle have certainly enjoyed more positive moments in their six games than Erik ten Hag's Manchester United, who lurched from one bad result to another in Group A. Anthony Gordon, Bruno Guimaraes and the 17-year-old midfielder Lewis Miley have all shone in the Champions League and Newcastle have the resources to strengthen in January and qualify for next season's competition.

But when the groups are assessed, Newcastle suffered the same fate as United and there really is no upside to that, especially when the respective failures of the two clubs are likely to result in England missing out on a fifth Champions League spot next season.

With United sixth and Newcastle seventh in the Premier League right now, it would be ironic if their group stage exits leads to one of them missing out on qualification with a fifth-place finish in May.

Naivety at times cost Newcastle, both in terms of Howe as a rookie coach in the competition and players who lacked the experience of their group opponents.

"We wanted to qualify for the knockout stages for sure," Howe said. "That was very much our intention. Milan's goals came from mistakes; that can happen in any situation and I take ownership of that, but I'd much rather make mistakes while trying to go for a win.

"With any setback, though, you have to use it as fuel. Any pain today we have to use as motivation for tomorrow."

That's Newcastle's only option now, though. Without even the Europa League to look forward to, Howe and his players have plenty of time to reflect on their Champions League campaign and how qualification was so near, but ultimately so far.