Duckett impressed as he hit a crucial 60 from 78, building a 153-run partnership with Ben Stokes as England recovered from 63 for three to make 309 for eight.
Bangladesh then collapsed in reply, going from 271 for four to 288 all out as England won the first ODI by 21 runs in Dhaka.
And that ensured it would be a dream debut for Duckett, who drew praise from his captain.
“It looks like we’ve found a player there,” said Buttler.
“The greatest compliment you could pay him is that you’d never know he was on debut at all. He looked like he was a seasoned pro out there.
“He and Ben (Stokes) showed exactly the kind of things we want to be about. We were 63 for three and could easily have dug a hole for ourselves but the fashion in which they built that partnership was fantastic.”
Sky Sports pundit Nasser Hussain was also impressed with Duckett.
Hussain said: “Here’s a 21-year-old on debut and he was ice cool.
“Stokes was sweating at the other end and this little lad was under immense pressure, but he was cool, he was calm and he played his way.
“A lot of people come into international cricket and think they’ve got to bat like Ben Stokes, got to be belting it out of the ground, but he didn’t.
“He played his way and he was very honest as well, saying he lost a bit of rhythm towards the end and he’s going to look at it.
“He’s another person who isn’t one dimensional and when spinners are on, he can knock it and manoeuvre.
“He reminds me a little bit of how Eoin Morgan was when he first came into the side in that as a captain you’re thinking ‘he can reverse sweep, I’ve got to move that man’.
“As an opposition captain he’s one of these players who you’re always looking for an extra fielder to cover because he can hit it 360.”