Abraham's missed penalty during the shootout ensured Jurgen Klopp's side were the winners in Istanbul following a 2-2 draw and the ex-Aston Villa man was later the victim of abuse on Twitter.
Lampard praised Abraham's bravery in stepping up to take the fifth penalty and said it is "too easy" to send abuse on social media platforms.
"I am particularly disgusted by a so-called Chelsea fan," he said. "To see the different ends of the spectrum of the evening, Tammy Abraham asked me to take the fifth penalty, because he wanted to take it, wanted to stand up, wanted to be brave on a big night when the world is watching.
"At the same time, within moments, somebody sitting behind a keyboard or a phone has said the most disgusting things possible you can say.
"I don't know how on these platforms it's allowed that people can do it. It's too easy to be done so something needs to be done as well as changing people's mindsets completely.
"That might not be easy with everybody, but I'm so angry for Tammy, angry for us as a club because that's not what we're about. The club does a lot of work against discrimination at all levels and it's a setback when these things happen."
European football's leading anti-discrimination organisation Fare network have urged Twitter to take more responsibility in combating incidents of racism on the social media platform.
"The Fare network is aware of reports of racist abuse aimed at Tammy Abraham on social media after Chelsea's UEFA Super Cup match against Liverpool," a statement to ESPN FC read.
"Social networks such as Twitter continue to shirk their responsibilities when it comes to monitoring and preventing online abuse. It is all too easy for individuals to tweet hate speech with impunity. The measures being taken by the platforms are simply not effective, they need to do much more.
"Fare stands in solidarity with Tammy Abraham and other victims of racial abuse online."
Information from ESPN FC's Andrew Cesare Richardson was used in this report.