The burly Australian is used to upsetting the world order of international cricket - in 1996, he coached Sri Lanka to the World Cup title.
"We can't just sit back and say, 'that's it, we have answered our critics and that's the end of the story'. Far from it," said Whatmore.
"We have still got a long way to go yet and the reality is that Bangladesh are still the number nine side in the world and, as sometimes happens, we put in a shocking performance and we get beaten heavily.
"When that happens, it leads to more comments (from the critics).
"We know that within ourselves we have improved and that we are capable of causing upset wins and we would like that to continue."
Bangladesh's win over India in the first round helped dump Rahul Dravid's side out of the tournament while Saturday's 67-run win over South Africa in Guyana threw the race for the semi-finals wide open.
If Bangladesh were to beat England here on Wednesday, they would become outside contenders for a last four place themselves.
"The win against South Africa gave us a lift but we are not getting carried away," said Whatmore.
"Everyone who saw the game in Guyana knows that conditions there were very different to the ones we encountered in Antigua (where Bangladesh lost to Australia and New Zealand)."
Whatmore was referring to the slow Georgetown pitch which was ideally suited to left-arm spinners Mohammad Rafique, Abdur Razzak and Saqibul Hasan who took seven wickets between them.
The pitch at the Kensington Oval here is expected to have pace and bounce.
But England batsman Ian Bell, whose team need to win all of their three remaining matches to stay in contention for a semi-final place, said that Bangladesh will not be under-estimated.
"Bangladesh are a fantastic side and we are not treating them as minnows," said Bell.
"We know they have talented young cricketers and they have proved that thay can play against some of the best sides in the world."