Trott struggled on his return to the Test arena during England's 1-1 drawn series with he West Indies in the Caribbean concluded Sunday, managing just 72 runs in six innings including three ducks.
"This was a tough decision to make but I don't feel my game is at the level you need to be at to play for England," said Trott yesterday in an England and Wales Cricket Board statement.
"I was honoured to be given the opportunity to come back and play international cricket again and I'm disappointed it didn't work out.
"I also want to wish the lads all the very best for what will be an incredibly exciting summer."
The 34-year-old Trott, who intends to continue his county career with Warwickshire, added: "I've had incredible highs and some real lows in an England shirt but wouldn't change a thing.
"I look forward to continuing my career at Warwickshire and hopefully helping us win more silverware."
The West Indies series saw Trott recalled by England for the first time since his premature exit from the 2013/14 Ashes series in Australia following the first Test in Brisbane with what team officials later said was "situational anxiety".
"He can be incredibly proud of all he has achieved in his career and it is no coincidence that his time in international cricket has seen the team achieve some very special things often with Trotty at the heart of our success on and off the field."
Cook added: "To come back from events around the Brisbane Test in 2013 and earn a place back in this side is testament to his character and spirit, and although things didn't work out as we all hoped on this current tour, he gave absolutely everything to the Three Lions every time he wore the cap.
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