In a statement released via Instagram on Thursday, the SexyBack singer apologised to his “amazing wife and family” for putting them through such an “embarrassing situation” – but insisted that nothing else had occurred between himself and Wainwright.
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“I stay away from gossip as much as I can, but for my family I feel it is important to address recent rumours that are hurting the people I love,” Timberlake wrote.
“A few weeks ago I displayed a strong lapse in judgement – but let me be clear – nothing happened between me and my co-star. I drank way too much that night and I regret my behaviour.
“I should have known better. This is not the example I want to set for my son. I apologise to my amazing wife and family for putting them through such an embarrassing situation, and I am focused on being the best husband and father I can be. This was not that.
“I am incredibly proud to be working on Palmer. Looking forward to continuing to make this movie and excited for people to see it.”
Last month, the married star was seen sitting on a balcony in New Orleans and holding hands with Wainwright, who at one point was resting her hand on his knee.
Timberlake, 38, wed Jessica Biel, 37, in 2012 and the couple became parents to son Silas three years later.
The pictures of the Palmer co-stars’ intimate moment sent shockwaves around Hollywood, with Timberlake and Biel considered one of the industry’s most rock-solid couples.
Neither Biel or Wainwright have publicly commented on the photos.