Kevin Pietersen said in his apology, "I truly didn't mean to cause upset or tension particularly with important games at stake".
The England batsman was dropped for the final test against South Africa - which begins tomorrow - after it came to light that he had sent derogatory texts to the rival team.
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Goals from Charlie Austin, Dusan Tadic and James Ward-Prowse consigned Slaven Bilic's men to their fourth straight Premier League loss.