The ugly, incontrovertible truth is that Manchester City faces an impossible task. It will try to keep its Champions League campaign alive by beating Ajax on Tuesday (2:30 p.m., ET, Fox Soccer Channel ). But even if City manages to keep its European campaign on life support for another few weeks, it almost certainly won't win the big-eared European cup this year.

Recent Champions League history is littered with expensively-assembled teams that never lifted the coveted trophy. Sugar daddies spent lavishly to secure national dominance. But on the European stage, it takes more. And teams that were bought to be brought together don't often have it.

Olympique Lyonnais , for instance, spent heavily throughout the past decade, financed by IT magnate Jean-Michel Aulas. Through a litany of inspired transfer dealings, Lyon won seven consecutive French titles from 2002 through 2008 but forever stumbled on the European stage, only reaching as far as the semifinals in 2009-10.

In the late 1990s, Sergio Cragnotti, the head of an Italian food giant, gobbled up all the world's finest talent for his Lazio club. Eventually, Sven-Goran Eriksson managed the likes of Hernan Crespo, Juan Sebastian Veron, Alessandro Nesta, Christian Vieri and Pavel Nedved to the 2000 Serie A title. But Lazio never even made it to the final four of soccer's big dance.

That isn't to say nobody has spent his way to European success. Real Madrid did it in 1998, 2000 and 2002, but it blended homegrown talent with exceptional ringers like Luis Figo and Zinedine Zidane. Several teams even managed to win it without a foundation bred in-house. Inter Milan did it in 2010. Chelsea won it last season. But both these entirely store-bought teams spent many years together, gelling and maturing, before finally conquering the continent.

Inter's backbone of Julio Cesar, Maicon, Walter Samuel, Javier Zanetti, Esteban Cambiasso and Dejan Stankovic, largely assembled by Roberto Mancini, the man who could never put them over the top, had been in place since the mid-2000s. With a few more acquisitions added to that base - Lucio, Wesley Sneijder, Samuel Eto'o and Diego Milito - Inter made its breakthrough under Jose Mourinho.

Chelsea, largely assembled by Jose Mourinho, the man who could never put them over the top, had been fielding its core of Petr Cech, John Terry, Ashley Cole, Frank Lampard, Michael Essien, John Obi Mikel and Didier Drogba continuously from 2006 onwards. It took half a dozen years for them to figure it out and finally win Europe's biggest game, having lost the final on penalties in 2008.

Which brings us to Manchester City, which will fight for its European life at home against Ajax on Tuesday afternoon. A fortnight ago, Ajax - a young, underfunded collective led by playmakers Siem de Jong and Christian Eriksen that has traditionally acted as the farm team of Europe's elite clubs - made a mockery of City in a 3-1 win when the score was predicted to be the reverse.

City's Abu Dhabi ownership is unapologetically ambitious and has spent accordingly, bringing in big names faster than Mancini could field them or the vast sums they laid down for them could be counted. Carlos Tevez came. Yaya Toure came. Kun Aguero came. David Silva came. Last year, they were rewarded with the Premier League title.

The next step? Europe. But, like last season, City's European campaign has been a disappointment. With just a point from their first three games and a five-point ravine to bridge in order to reach second place in the four-team group and advance, City just about needs to win all three of its remaining games.

Mancini, now in charge of City, has publicly given up on making a run at the Champions League crown, seemingly well aware of the precedent set by other spend-happy teams.

"I don't think we're ready to win the Champions League," Mancini said. "If we say we're ready to win it, we're not honest. ... We're a good team but we're not ready in the Champions League, like the other teams. Chelsea tried for 10 years to win the Champions League. They were probably the best team in Europe for 10 years and they won it [last May] after 10 years, probably when they didn't deserve to. They deserved to win it three or four years before. The Champions League is like this."

Beating Ajax, which looked dire in a 2-0 loss to Vitesse at the weekend, should be a straightforward assignment. But City was outplayed on the weekend too, drawing West Ham 0-0 in a game they really should have lost. And if City overcomes Ajax, daunting dates with Real Madrid and Borussia Dortmund await. It will probably need to win those two as well.

At Inter, Mancini's European futility wasn't tolerated. If City does anything other than win on Tuesday, it will fairly well bounce itself from the competition before the knockout stages for a second year running. Mancini has acknowledged that he feels the pressure from above.

"I think the owners are upset," he has said.

And if the club doesn't recognize that any manager will need time to build a team that has the necessary savvy and cohesion to compete in Europe, which can only come from playing together for many years, the same fate could soon befall Mancini in Manchester as it did in Milan.

Fair or not, Mancini is fighting for his job on Tuesday. And if it's dependent on European success, history suggests he will lose it.