Matthew Upson will deputise for King and Carragher against Slovenia and is likely to partner John Terry - who was first out on the training pitch as he attempts to move on from the headlines of the last few days - in the centre of defence.
"We need to get the best out of ourselves and that's an individual thing as well as a team thing," said Upson.
"It's down to us as individuals to make sure we are in the right frame of mind and let it flow, let it happen and hold nothing back."
"Everyone was disappointed after the Algeria game. We have had to put that behind us and move on to the next game. It's all down now to the game on Wednesday."
Other selection issues for manager Fabio Capello include whether to keep faith with striker Emile Heskey or bring in Tottenham's Peter Crouch.
Capello could also consider a switch in formation, playing five in midfield, with Joe Cole or Shaun Wright-Phillips likely to come into contention.
England are without a victory at World Cup 2010 after drawing 1-1 with the United States in their opening game before being held to a goalless draw by Algeria on Friday.
A defeat against Slovenia would mean England are eliminated, while a draw would leave their fate depending on the result between the US and Algeria. Victory sends Capello's side through to the last 16.
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