The 2019 champions were eliminated after their sixth defeat in seven matches and Buttler's own form was emblematic of his team's struggles in the showpiece event.
White-ball stalwart Buttler has not managed a single half-century in seven matches so far, while England have reached a 200-plus total only twice in their last five matches, all of which they lost.
"My own form has been the biggest concern," wicketkeeper-batsman Buttler said at the post-match presentation ceremony.
"Coming into the tournament I felt in a great space. So to have not played as well as I can in such a pivotal role is disappointing.
"My own performance with the bat has hurt us."
Having won the T20 World Cup in 2022, England arrived in India as one of the pre-tournament favourites, but their batting has been a huge letdown in the tournament.
Buttler had no hesitation in calling their elimination "a low point".
"To be stood in this position having arrived in India with high hopes is incredibly tough and disappointing. It hurts a lot.
"We haven't done ourselves justice. Coming into the tournament we fancied ourselves to have a real go and push.
"We've let ourselves down. We've let down people at home, who support us through thick and thin and we wear that on our own shoulders."
In what would have sounded improbable at the start of the World Cup, England are now fighting for a top-eight finish to try to qualify for the 2025 Champions Trophy in Pakistan.
"The only way to get back into form and winning games is to front up and go again," Buttler said, dwelling on their next game against the Netherlands on Wednesday.
