"Women have a harder time being seen as legitimate", Ocasio-Cortez said, referring specifically to Nixon and NY state attorney general candidate Zephyr Teachout, all progressive candidates who join Ocasio-Cortez's call to abolish ICE.
She joined protesters at the Standing Rock demonstration against a natural gas pipeline.
Pundits are questioning whether Ocasio-Cortez's upset spells trouble for Pelosi, but Thompson said her fate hinges on the November elections. The district includes parts of Queens and the Bronx.
Ocasio-Cortez has also been at the front lines - literally so, last weekend, when she traveled to join protests at an ICE detention center in Texas - of the progressive backlash against the Trump administration's border and immigration policies. "Oh my God", she repeated.
"I felt like our party could be better, our message could be better, and that we could be better as a country", she said. Earlier this week, Pressley called for defunding the federal Immigration and Customs Enforcement, which she said "is creating an atmosphere of toxic fear and mistrust in immigrant communities".
The district has been represented by Democrats since 1993.
The 10-term Democrat raised $3 million, compared to his opponent's $200,000.
The upset win, which quickly spread across social media and caught the attention of the country, was seen as a major challenge to the Democratic political establishment, since Ocasio-Cortez ran a largely grassroots campaign and was outspent by an 18-1 margin, according to the Associated Press.
Trump denies he's to blame for Harley-Davidson decision
Wisconsin's elected leaders said the decision pointed to the need to expand markets. The EU has responded in kind, levying a tariff on several American products.
Alexandria Ocasio-Cortez represents something new in national politics in the United States-a Latina millennial entering power with a bold, progressive agenda.
Pelosi, who is under pressure to step aside and pave the way for a new generation, insisted that the victory for the left wing of the party was not representative of a wider trend. In April, a secret recording was leaked, of House Minority Whip Steny Hoyer telling progressive candidate Levi Tillemann, who was running in Colorado's Sixth District, that he should get out of the race to make room for Jason Crow, the candidate favored by the Democratic Congressional Campaign Committee. "It is not to be viewed as something that stands for everything else".
"I am female. I am progressive. What's your problem?" Pelosi replied with a laugh, "two out of three ain't bad".
The New York primary was not the only vote on Tuesday.
Unlike the other insurgent candidates, Ocasio-Cortez was able to convince enough voters to vote for a new face instead of a 20-year incumbent.
And in Colorado, congressman Jared Polis's primary victory could see him elected as America's first-ever openly gay governor. He ran on a left-wing platform, including single-payer health care.
Jealous will face incumbent Republican Gov. Larry Hogan in November.
History suggests Mr Trump's Republican Party, like the parties of virtually every first-term president dating back to Ronald Reagan in 1982, will suffer losses this autumn.
On the Republican side, President Trump continued his winning streak, as candidates he endorsed once again won their races.