Morgan and batsman Alex Hales both decided not to go on the tour as they were concerned, despite reassurances from team security chief Reg Dickason after he came back from a fact finding trip, over their safety.
The tour — which begins on September 30 and will include two Tests and three ODIs — had been called into question after an attack on a cafe in Dhaka in July which saw 20 hostages killed, including 18 foreigners.
Morgan especially came in for some criticism over his decision — former captains Michael Vaughan and Nasser Hussain leading the charge with both questioning whether he could resume being skipper.
Test captain Alistair Cook by contrast has said he will skipper the side against the Bangladeshis.
However, Buttler said the former captains’ speculation over Morgan’s future was nonsense.
“He’s very much still the captain of the England ODI side,” said Buttler.
“He’s done a fantastic job over the last 18 months.
“He’s been one of the main reasons, if not the main reason, for the turnaround in fortunes.
“The style of cricket he’s got the side playing is something we want to continue and keep playing that brand of cricket,” added the 26-year-old.
Buttler, who made his ODI debut back in 2012, said Morgan would have not taken the decision lightly.
“There has been some unfair criticism,” he said.
“Cricket is not the be-all and end-all.
“He has made the decision that is right for him and it is not one he has taken lightly. He has come to one which he is comfortable with and people should respect that.
“Reading things in the press and having a lot of information about it, you do have some worries. But you try and think long and hard about it, let the dust settle for a bit and try and work through it logically.
“For me personally I’m happy to go.
“It’s a completely individual position, as it has to be; people are different and view things differently – and everyone completely respects that it is a personal decision.”
Last week saw Morgan outline his concerns, with the 30-year-old Irishman saying he had been influenced by a bomb exploding at a 2010 Indian Premier League match in Bangalore that he was involved in and the violent background to his brief spell in the 2013/14 Dhaka Premier Division.
Morgan, has however, since returned to India for further spells in the lucrative IPL.