The Tigers claimed the last spot in the Super Eights second round stage by surviving a scare against Nepal who faltered in pursuit of just 107 on Sunday.
For a country known for its wristy stroke players, Bangladesh have just one batsman in the top 20 at the tournament.
Towhid Hridoy has made 95 runs in four innings while only former skipper Shakib Al Hasan has managed to hit a 50.
In their loss to group winners South Africa, Bangladesh fell short by four runs, chasing only 114 to win.
"It's not happening and it is not acceptable," said Shanto.
"It is not possible that every day the bowlers will make the team win. I hope they make us win every day, that's what I hope for but the batsmen also have a responsibility.
"And why it is not happening, everyone is trying to find out. To be very honest, I think the wicket is not the issue. It is definitely a reason for us to worry."
It has been Bangladesh's bowlers who have bailed the team out on a regular basis at the tournament.
Ahead of Monday's concluding two games in the first round group stage, they have four bowlers in the top 20.
Fast bowler Tanzim Hasan Shakib has nine wickets with a best of 4-7 while fellow seamers Mustafizur Rahman and Taskin Ahmed have seven apiece.
Leg-spinner Rishad Hossain, like Tanzim just 21 years old, also has seven wickets.
"We have to come out of this and we have to think about how to come out of this. We plan and think about this all the time," added Shanto.
"I hope that we can reduce these mistakes in the next round."
In the Super Eights stage, Bangladesh face Australia and India in Antigua on Thursday and Saturday respectively before taking on Afghanistan in Saint Vincent on June 24.
