Parris scored the opening goal in a 6-0 win against Russia in September 2017 and ran towards the dugout to celebrate with Sampson, who was facing accusations of discrimination and bullying by Aluko and team-mate Drew Spence.
Sampson was later sacked by The FA a day later due to "inappropriate and unacceptable behaviour" in a previous position but was cleared of the allegations made by Aluko and Spence.
"Eni, I am sorry that my thoughtless actions caused you hurt, never is it in my conscious intentions to make another human feel devalued," Parris, 26, wrote on Twitter.
"At the time I focused more on what I believed was showing unity when really it did nothing of the sort."
Parris then conceded she has been reflecting on how she can affect positive change.
Her comments come amid worldwide anti-racism protests following racial injustice, including the death of George Floyd, an unarmed black man who died in police custody in Minneapolis on May 25.
"I am a proud black woman, I understand I have a social responsibility to help create change through my platform," Parris added.
The FA lated issued a public apology to Aluko and Spence in October 2017 while Sampson followed suit in January 2019.
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