With a 2-0 lead already secured from the Dhaka leg, England had already become the first away team to win a bilateral ODI series in Bangladesh since Buttler himself oversaw a 2-1 win in 2016-17.
Despite limiting Bangladesh to 246 in another impressive bowling display, in which Rehan was the only player to serve up his full allocation of ten overs, England were eventually undone by the proven wiles of Shakib Al Hasan, who top-scored with 75 from 71 balls before stifling the run-chase with the fine figures of 4 for 35, including his 300th in ODI cricket.
"Those numbers speak for themselves, don't they?" Buttler, England's white-ball captain, said. "Playing against him, you know what a great challenge it is. If you go back to the 2019 World Cup, his performances were outstanding. He's a brilliant player."
Buttler, however, was undeterred by the loss, and insisted that the nature of England's wins in the first two games - in particular the hard-fought centuries from Dawid Malan in the first game and Jason Roy in the second - had given his team ample pointers as to the approach that could prove successful on similar wickets in India this winter.
"We changed a few things today and gave an opportunity to people in different ways, but I thought the intensity was still there," Buttler said. "We certainly believed we could win the game, and if we played well enough, we would have won the game.
"But there was an opportunity today to give Rehan a debut, and for Sam to bat at No. 5, and this is the last ODI we play now until September. So, especially in these conditions, it felt like a great chance to gather as much information as we can, and expose people to different situations. If we lost the game, then so be it. But I certainly believed we had a team and a performance that could have won the game today."
Buttler's phlegmatic attitude reflects an ODI cycle in which England have consistently struggled to field their first-choice XI. Rehan's selection made him the 39th different player that they've used in 36 matches since their victory in the 2019 final, while England's record in that period, 18 wins and 15 losses, is similarly hit and miss.
However, Buttler added that England's victory in the T20 World Cup in Australia before Christmas - which was achieved in spite of a similarly disrupted build-up - had given him confidence that the squad that comes together in India in seven months' time will be able to call upon similar experience to overcome their lack of physical preparation.
"I think the schedule is hugely challenging to always get your best XI on the field," Buttler said. "But the game has changed a bit [since] the previous cycle of the World Cup.
"Looking back to the T20 World Cup, we probably went into that World Cup having never played our perceived best XI. But then to get into the tournament and go on to win it, that gives you great confidence that, even though we haven't had the opportunities to always play our best team, international cricket has become [more] focused on the ICC tournaments. I think that's the way we're building towards that. And we know that, come the World Cup, we will have the opportunity to pick from everyone who's available."
England's first-choice batting unit has been especially depleted in recent months, with Ben Stokes retiring from 50-over cricket due to the relentless demands on England's multi-format players, and Joe Root also absent from this tour because of the clash with the recent Test series in New Zealand. Had he not already been ruled out with a broken leg, Jonny Bairstow would also have missed this tour for the same reasons.
And so, this third ODI was arguably of greatest significance to the likes of Phil Salt and Vince, two of the batters who would appear likeliest to make way in a full-strength squad. Salt was visibly furious with himself when he failed to convert a bright start of 35 from 25 balls into a more substantial performance, while Vince's 38 from 44 balls was a similarly unfulfilled display.
"Everyone is desperate to play well, whether you're an established player or whether you're someone who's potentially seen as on the fringes," Buttler said. "We know there's huge quality in those guys, and it's great to expose them to these conditions but, I think, if you're looking at the game today, we needed someone to go on and really take ownership of that chase.
"One great learning is, when you lose a couple of wickets in clusters in these kinds of conditions, it's a good time for the opposition to really squeeze you and you feel under pressure. So when you look at the first two games, Malan taking the game all the way through and Jason Roy playing a long innings to score a hundred, yeah, we maybe just missed someone today going on and playing that match-defining innings."
Buttler insisted that England had not lacked "intensity" in their performance, but acknowledged that they had taken the "opportunity" of the dead-rubber scenario to experiment with their options. This included giving Rehan a full quota of overs (England's eventual player of the series, Adil Rashid, bowled just five) while Curran was given the chance to respond to a tricky situation with the bat, after a 54-run opening stand between Roy and Salt crumbled with the loss of three wickets in the space of eight balls.
"He doesn't lack confidence," Buttler said, after Rehan - at 18 years and 205 days - had struck with the final ball of his spell for the debut figures of 1 for 62. "He's very trusting in his ability, which is fantastic for a young guy, and he was willing to bowl to very aggressive fields and challenge himself, which is a great sign moving forward. For a guy on debut, I thought he handled himself brilliantly well.
"We are blessed with a lot of allrounders in our squad, and it felt like today was a good chance to use them all," Buttler added. "I see huge potential in Sam Curran's batting and today there was an opportunity for him to get higher up the order. So yeah, that's the thinking behind it.
"We played some really good cricket throughout the series, and I've spoken a lot about these being great conditions for us to challenge ourselves in.
"These are probably the conditions that we would find the hardest as a team. Bangladesh are a tough side to beat in their own conditions. So to win the series, there's plenty to learn. Things that we've done well and areas that we can also improve."
Andrew Miller is UK editor of ESPNcricinfo. @miller_cricket