The 24-year-old, who made 71 runs in the draw at Trent Bridge, did not break any team rules but will be 'reminded of his responsibilities' by his coach.
"I am aware that some of the England players were caught on camera relaxing after the conclusion of the recent Trent Bridge Test match," Moores is quoted as saying by Sky Sports News.
"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."
Ballance made his Test debut earlier this year against Australia.