The veteran midfielder delivered his message after goals from Jude Bellingham and Harry Kane secured a 2-0 victory over Panama, a result that saw England finish top of Group L and book a Round of 32 clash against Democratic Republic of Congo in Atlanta on Wednesday.
Despite winning their group, England have yet to hit top gear in the tournament. A chaotic but thrilling 4-2 victory over Croatia was followed by a laboured goalless draw against Ghana before they were frustrated for long periods against the lowly-ranked South Americans.
The Three Lions reached the last two European Championship finals and the semi-final of the 2018 World Cup, and expectations remain high that Thomas Tuchel's side could go further in North America.
Yet Henderson insists England need to "stay in the moment" as they bid to make history.
"I think we're in a good place... it's just staying calm and staying in the moment, not getting too carried away," he told reporters when asked what lessons England could learn from previous tournaments.
"Just focus on what we need to do, what each person's job and role is, and making sure that we're doing it to the best of our ability. And then helping the team around, giving absolutely everything for each other."
The 36-year-old made history against Panama as he became the first England player to appear at four World Cups and believes his experience can play a crucial role in guiding the squad's younger players through the latter stages.
"I'm just delighted to be a part of this team, and it's still as special now as it was when I made my debut in 2010," he said.
"Time goes quickly, but I'm just delighted that I can help the teams as much as possible, both on and off the field, and just try and give everything I can to help us achieve our dreams, really."
England are one of the favourites to win the trophy but DR Congo, playing in their first World Cup since 1974, have already pulled off one huge upset by drawing against Portugal in their opening match.
Their team features several Premier League players including West Ham's Aaron Wan-Bissaka, Sunderland's Noah Sadiki and Newcastle's Yoane Wissa, who scored against Portugal and twice in the 3-1 victory over Uzbekistan which clinched their place in the last 32.
"I see in the first game they got a good result against Portugal, I think it was Wissa scored. We know him well, good team, some good players. Very, very strong," Henderson said.
"In the knockout rounds (there are) no easy games."