Only Joe Cole, Salomon Kalou and Jon Obi Mikel remained from the team that defeated Arsenal on Sunday.
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Jon Obi Mikel almost deflected Dean Whitehead's near-post cross past Cudicini but the home side's best chances fell to Jones.
Even so, Kalou, Jon Obi Mikel, Joe Cole, Ballack and Zhirkov all either forced regulation saves from Robinson or missed the target before the break.
Pereira, who had been needlessly booked for dissent, was shown his second yellow for a studs up challenge on Jon Obi Mikel to leave his side with an uphill task.
Chelsea were partial architects of their own downfall as Jon Obi Mikel headed a long Bridge clearance towards his own goal but Tevez then repeatedly managed to hold off both Terry and Ricardo Carvalho before shooting limply beyond the outstretched but ultimately futile dive of Hilario.
The second chance came just before the interval - from West Ham's first corner - when Matthew Upson headed the ball on and Tristan flicked the ball goalwards only for Jon Mikel Obi to clear off the line.
But he was left to rue the fragility of the defence in front of him when Jon Mikel Obi's long ball was chested down by Drogba, who then held off Finnan and fired in at the near post.
But unlike in the Carling Cup final, this time Villa did not get a penalty when the striker was brought down by Jon Mikel Obi, who was in all likelihood the last man as it seemed Paulo Ferreira was unlikely to get across and cover.
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Villa responded to losing 7-1 to the Premier League leaders a fortnight earlier with a performance of industry and desire and their manager Martin O'Neill will also believe his side should have had a first-half penalty when Jon Mikel Obi clumsily felled Gabriel Agbonlahor inside the area.
The charge relates to the conduct of the players towards referee Mike Dean after he sent off Mikel Jon Obi.
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The Ivory Coast duo Didier Drogba and Salomon Kalou, Ghana's Michael Essien and Nigeria's Mikel Jon Obi are all expected to play at the tournament.
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Mikel Jon Obi, Arjen Robben and Wright-Phillips were struggling to get in the game and Norwich, with Etuhu and Darren Huckerby to the fore, were posing problems.
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