Yorkshire batsman Ballance, who made 71 in the game, went out following the end of the series opener on Sunday night, along with several team-mates, and was snapped by members of the public enjoying himself in the early hours.
Despite being in the middle of back-to-back Tests - with hostilities due to resume on Thursday at Lord's - Moores gave his squad permission to go out ahead of a rest day on Monday.
But the pictures are clearly ones the England and Wales Cricket Board would not welcome as a regular occurrence and Moores has vowed to talk to the squad about his expectations for their public appearances.
Moores said: "I am aware that some of the England players were caught on camera relaxing after the conclusion of the recent Trent Bridge Test match.
"As the players had been released at the end of the first Test and were not due to meet up to begin preparations for the second Test until Monday evening, and there were no suggestions of impropriety, there is no need for any disciplinary action.
"I will however be reminding all players of their responsibilities to uphold the best possible image for England cricket."
- Sports & Recreation