Bangladesh's fielding was also catalyst in their 16-run win in the third match, a result that helped them whitewash England.
The turning point of the match was the run-out dismissal of Buttler. England coach Mathew Mott even said he didn't expect such an electrifying fielding.
"It was a pretty freakish run-out. I was actually looking at the other end and then all of a sudden the bails lit up. Full credit, that was a real turning point," Mott said.
England were on course of a victory, thanks to Buttler and Dawid Malan after Bangladesh put up 158-2. But their dismissal in consecutive deliveries helped Bangladesh hit back into the game.
Shakib said they showed the character, something they wanted to show in this series to make a statement.
"We talked about showing character ahead of the series and that's what we showed," the Bangladesh skipper added.
"We were put into tough position but won the game. That's the thing that would give us the confidence as we are trying to build a team for the 2024 T20 World Cup."
He further said the performance in the last T20 World Cup changed them as a team in this format in which they were vulnerable most of the time.
"We showed out gutsy performance in the last T20 World Cup even though we couldn't win against big teams but we created opportunities to win the matches. That gave us the boost," he opined.
"The last World Cup changes us. We were really good in this T20 series, fielded well, bowlers were good, batters contributed. We have to build on from here for the (T20) World Cup next year."
"We batted really well on a tricky wicket, credit to Litton and Rony, we were happy with the total, and had to stick to our plan. That over to get two set batsmen out in two balls changed the game completely. From then on we had the momentum. Ireland will be another challenge for us, we have to continue this performance."