The BBC Breakfast presenter was found to have been in breach of editorial guidelines for speaking out on air about comments made by the US president, which were widely condemned as racist.
Ms Munchetty told co-presenter Dan Walker: "Every time I have been told, as a woman of colour, to go back to where I came from, that was embedded in racism," adding: "I'm not accusing anyone of anything here, but you know what certain phrases mean."
Mr Trump had called for a group of ethnic minority Democrat congresswomen to "go back" to their own countries.
A petition launched by a group called Dope Black Dads - a black father's organisation - had this morning topped 13,360 signatures and was close to achieving its target of 15,000.
In a statement posted alongside the change.org petition, the group said: "The Editorial Complaints Unit's decision is wrong and has three implications.
"First, the decision suggests a serious lack of diversity in the organisation. It demonstrates that even with a limited increase in diversity in certain areas, it does not see to have been matches with a similar increase in inclusion.
"Second the decision, if not handled properly, could have a seriously negative effect on BAME (Back Asian & Minority Ethinic) staff working in the organisation.
"Third, if the most senior levels of management do not respond publicly to the decision, it may well have a seriously negative effect on the BBC's reputation and credibility vis-a-vis large parts of its audience for years to come."
The statement added: "I think the BBC could use the ECU's decision as an opportunity to build trust as well as strengthen its diversity and inclusion.
"All - senior members of hte BBC should make their position clear and come out internally in support of Naga.
"I also suggest senior management goes further, so as to ensure public credibility. Ideally the most senior levels of BBC should make a public statement about the ECU's decision, and use this as an opportunity to reiterate the importance of diversity and inclusion at all points of the organisation."
Trevor Phillips, the former chairrman of the Equality and Human Rights Commision, said BBC staff and presenters had been prevented from joining a protest in support of Ms Munchetty.
But Newsnight presenter Emily Maitlis went ahead to criticise the judgement despite the warning from BBC management.
"My worry is that the complaints body looks as if it's massively out of touch what what's happening in the real works," she told the Cliveden Literay Festival in Taplow, Berkshire.
"If you have a woman of colour in a prominent position in a main news outlet, who is a presence but somehow not allowed to be a voice, that's a very difficult place for her to be. I just think it shouldn't be my colleagues, people of colour, having to come out and say this. It should be all of us."