The left-back posted on Instagram after the 2-1 win at Tottenham Hotspur Stadium, with several people responding with monkey emojis and racist comments.
Tottenham have now condemned the abuse, promising to take action against the brazen perpetrators.
In a statement on Monday, the club said: "We are disgusted at the racist messages directed towards Destiny Udogie on social media following Saturday’s game against Liverpool.
"We will work with the Premier League and, where possible, take action against any individual we are able to identify. We stand with you Destiny."
The 20-year-old left-back featured prominently in the remarkable victory for Spurs, performing strongly against Mohamed Salah and drawing two challenges from Diogo Jota in the space of 22 seconds that earned the Portuguese attacker a red card in the second half.
The match was mired in controversy overall, with the VAR Darren England failing to realise that a legitimate Luis Diaz goal had been ruled out for offside with the score at 1-0 to Tottenham, in a damning breakdown in communication. The PGMOL has since acknowledged the error, but Liverpool have deemed their explanation 'unacceptable'.