Striker Abraham, 21, was targeted on social media after his side lost 5-4 on penalties after the match ended 2-2.
“Such abuse is now increasingly predictable, but no less disgusting,” said Kick It Out.
“We send our support to Tammy and reiterate our call for Twitter and other social companies to clamp down on this level of abuse.
“This is a call to action – we want to know what they are going to do to tackle this insidious problem.”
It comes after there were four reported cases of racist abuse on the opening weekend of the EFL season.
James McClean of Stoke City, Coventry striker Theo Robinson, Bambo Diaby of Barnsley and the sister of Fulham defender Cyrus Christie were all involved in incidents of ‘discriminatory abuse’.
Kick It Out also produced a report which was released in July which showed that reports of racist abuse increased by 43% last season, with 274 cases compared with 192 the previous season.
In one of those, Chelsea suspended six fans for using “abusive language and threatening and aggressive behaviour” towards Manchester City and England player Raheem Sterling during a Premier League match at Stamford Bridge in December 2018.
One of those fans was banned for life for using “racially abusive language” towards Sterling.