Along with Essex batsman Kishen Velani, Duckett, who has captained the side in the past, was withdrawn after failing to meet the required fitness standards and Smith said that the lapse was unacceptable.
“He stated: “Obviously he’s not fit enough and there are no excuses for it whatsoever.
“I’m disappointed in him, not for him, and he’s not grasped the need to meet fairly basic standards.
“We pride ourselves at this club on our sports science and making sure our cricketers are fit for purpose.
“It’s not as if he didn’t know what was required and they are all well versed in this area.
“Everybody has to be responsible for their own actions and in simple terms, at that age, you should be passing these tests.”
Both Duckett and Velani will be given a further oportunity to meet the necessary standards before the squad for the U19 World Cup in January is selected.