"It is both disgusting and completely intolerable that anyone could be subjected to the racial abuse that Junior has received," Blake said in a statement on the club website.
"I am astounded that people believe writing and posting these comments is acceptable.
"We will be contacting Twitter and the Football Association for their help in identifying the individual concerned, and will pursue the strongest possible action against them.
Junior Stanislas received abuse on social media
"We strongly believe that social media platforms need to take greater responsibility and accountability for the actions of their users and the content that is published on their platforms.
"We would wholeheartedly support any movement towards ensuring that all social media accounts are verified through formal identification, and therefore make the users liable for their actions.
"The club's stance on any form of discrimination is unequivocal. It is completely unacceptable and must be called out and acted upon whenever and wherever it is found.
"We are a club which celebrates equality, diversity and inclusion, as highlighted by our ongoing 'Everyone Together' campaign, which tackles prejudice and promotes understanding.
"We stand firmly with Junior and will continue to work tirelessly to educate and rid the game of all forms of discrimination."