Bangladesh recently won the tri-nation series against Ireland and West Indies - their first-ever multi-team tournament trophy.
But the Tigers face South Africa, New Zealand and England in their first three matches of the World Cup.
"It will be difficult for us because our opponents in the opening three games are extremely strong," Mashrafe told reporters.
"To get a positive result against them won't be easy."
Bangladesh twice beat West Indies in the tri-nation series in Ireland, including the final.
Mashrafe said the tri-series win and Bangladesh's run to the semi-finals in 2017 Champions Trophy have raised expectations of fans.
"In the last five to seven years, people have started to come to watch us with expectations that we will win," he said.
"All I can say is that the World Cup will be a different ball game. If you follow cricket in England, you will see that a lot of runs are scored. It will need a different approach."