Matt Roller is an assistant editor at ESPNcricinfo. @mroller98
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The margin of victory was enough for England to move from the foot of the table, leapfrogging the Netherlands, Sri Lanka and Bangladesh on Net Run Rate (NRR). They may now qualify for the 2025 Champions Trophy even if they are beaten by Pakistan at Eden Gardens on Sunday, an outcome which would alleviate the pressure on both Buttler and coach Matthew Mott.
Key, England's managing director of men's cricket, spent two weeks with the team earlier in the tournament and has now returned to India. He will meet with both Buttler and Mott in Kolkata, where selection for three ODIs and five T20Is against West Indies next month will be on the agenda.
Buttler has been unable to pin down the causes of England's struggles at this World Cup and has taken significant responsibility himself, having endured an abject tournament with the bat. He has managed 111 runs at an average of just 13.87 in eight innings, a sequence extended on Wednesday by a tame chip to mid-off for 5 off 11 balls.
But he confirmed his intention to continue as captain in both white-ball formats after England's win. "I'd like to [lead in the Caribbean]," Buttler said. "I know Rob Key arrives in India today. We can have some good conversations with him and the coach and everyone, and make a plan for that tour. But yeah, I'd like to."
Buttler conceded that he was "very frustrated" with his own form. "You want to lead from the front and do that in your own performance," he said. "I'll stick to the stuff that's served me well over a long period of time when I've had these little runs of form and hopefully I'll come out the other side of it very soon."
England are likely to make several changes to their ODI side for the Caribbean tour. Zak Crawley, Ben Duckett, Ollie Pope, Will Jacks and Rehan Ahmed are among the young players expected to feature in a squad that will bear close resemblance to the one that beat Ireland 1-0 in late September.
The T20I squad will be stronger, with England only due to play four further matches in the format before the T20 World Cup in the Caribbean and the US next June, where they will attempt to defend the title that they won - under Buttler and Mott's leadership - in Australia last year.
Eoin Morgan, Buttler's predecessor, described England as "a sinking ship" on Wednesday afternoon but Buttler insisted that the squad have "stayed really close". He said: "If you watched training yesterday, the guys probably trained as hard as they have trained all trip, which shows the level of commitment and desire to put things right.
"It would be easy for us to tail off… credit to everyone for still putting [effort] in and showing how much it means to play for England and the pride in our performance. Of course, the Champions Trophy is something we're very focused on and determined to make sure we're there."