And it nearly happened early in the extra session when John Stones rose to meet a corner kick, only for Vrsaljko to clear the goal-bound header off the line.
Within the first five minutes, English fans were given cause for celebration when Kieran Trippier scored a free kick, giving his side a dream 1-0 lead.
They were briefly silenced when Croatia equalised through Ivan Perisic in the middle of the second half.
Mario Mandzukic got the victor in injury time to put Croatia, with previously a tournament-best semifinal in 1998 to its name, one game away from winning it all.
Croatia now have the chance to win their first World Cup final when they face France in the final at 3am on Monday, NZ Time.
Henderson has been key to England's success in Russian Federation so far with his calm and precise distribution as well as a willingness to protect the back three.
Subs: Marcus Rashford (for Sterling, 74) 6, Danny Rose (for Young, 90) 5, Eric Dier (for Henderson, 97) 5, Jamie Vardy (for Walker, 112) 5.
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However, Ronaldo took out time to pen down a heartwarming letter for everyone at Madrid confirming his departure. Ronaldo scored 450 goals in 438 appearances for Marid, he won 15 trophies and the Ballon d'Or four times.
Other teammates - Harry Kane, Harry Maguire, John Stone and Ashley Young expressed looks of disappointment, as they left the football pitch to join their families in the stands.
England plays Belgium for third place on Saturday.
"That's right, I'm picking England to win another penalty shoot-out".
Asked what he would be demanding from his players, the England coach told ITV: "To be able to keep doing what we have been doing, play with real defensive discipline, good organisation, tactical awareness". The last time they won the tournament was in their home stadium in 1966.
It was his first goal for his country, England's 12th of the tournament and ninth from a set-piece, but they should have added more from open play as they revelled in the space they were being given in the first half.
"There was a spell in the second half when they got the goal and their tails were up, we had to weather the storm". But we've fallen just a bit short.
As the action went end to end, Croatia had its chances, too. "And I don't think after the six or seven weeks we have been together, that we could have given more". Knockout football is fine margins.
Much of England's attacking prowess has depended on Sterling's sizzling pace, which has also helped them to pose considerable threat on the counter. It's down to what we do behind the scenes, what we work on in training, all the hard work to get here. But Kane said the team could "hold our heads held high" as they "went further than anybody thought". "So tonight we weren't quite there, but the team will be stronger for that".