Brighton scored in the dying minutes after the 27-year-old Austrian national team player was muscled off the ball, enabling Georginio Rutter to make it 2-2.
Still seeking their first league win in 2026, Spurs are in 18th place with five games remaining in the season.
"Kevin Danso has been, and continues to be, subject to significant and abhorrent racist abuse on social media," Spurs said in a statement on the latest flare-up of racism that remains alarmingly common around European football.
"We have heard and seen vile, dehumanising racism. Behaviour that is without doubt a criminal offence. It will not be tolerated."
Spurs said they were reporting content to London's Metropolitan Police, other authorities and social media platforms. UK police are taking an increasingly hard line against those found guilty of racism, with arrests and bans, but are still struggling to stamp it out.
"We will push for the strongest possible action against each and every person we identify," Spurs added.
"Kevin has our complete and unconditional support as a player and as a person. No one at this club will ever stand alone in the face of this.
"Nothing about form or league position can ever excuse or explain racist abuse."
Danso said he had seen the comments directed at him on a weekend when the Premier League was promoting its "No Room For Racism" initiative.
"The racist abuse has no place in this game or anywhere. But it doesn't define me, and it won't distract me from what is important. I know who I am, what I stand for, and why I play," he said on Instagram.
"Now it's about staying focused, working harder, and coming back stronger for the next games."