The Dutch drew 1-1 with the USA to finish ahead of them atop Group E. The Americans were then eliminated by Sweden in the last 16, the first time in history they had gone out before the tournament semi-finals.
"The first moment when I heard that they were out, I was just thinking yes, because from the start of this tournament, they have already a really big mouth, they were talking already about the final and stuff," said Beerensteyn, who scored in the Netherlands' 2-0 last-16 win over South Africa.
"I was just thinking you first have to show it on the pitch before you're talking. And I'm not being rude in that way. I have still a lot of respect for them. But now they are out of the tournament."
The Netherlands were eliminated in the semi-finals by USA at the World Cup four years ago.
"For me, yeah, it's a relief and for them, it's a thing that they have to take with them in the future," the Juventus striker said.
"Don't start to talk about something that's far away and I hope that they will learn from that."
The Americans have suffered a backlash since their shock exit. A pre-tournament ad by American World Cup broadcaster Fox Sports has been lambasted by fans as "arrogant."
The ad opened with the line: "The whole world is wondering, what's it going to take to stop this US team?" It then shows a number of national stereotypes including a Londoner riding a bus on a rainy day and an Italian in a leather jacket with binoculars, suggesting "Maybe we can steal their plays" as a drone with Italian flags flies over a USA training session.
