Bangladesh performed above expectations in their group matches when they stunned India in their opening game on way to qualifying for the second round for the first time, but have failed to keep up the momentum.
They are still without a point, having lost to defending champions Australia and New Zealand in their first two matches in the Super Eights.
"We don't want to finish at the bottom. We were not last in the whole tournament, but we are now at the bottom in the Super Eights," said Whatmore.
"Our objective is always to go higher (than Ireland), but the reality is that we are ranked number nine and we will be playing to change the rankings."
Bangladesh failed to test the opposition in their previous two matches as they lost to Australia by 10 wickets and to New Zealand by nine wickets, but Whatmore believed that side could have done better.
"Our objective is to push the opposition and this is what we want to do in the remaining matches," said Whatmore.
Bangladesh will meet England, the West Indies and Ireland in their last three matches.
"We need to up our performance in the second round," said Whatmore.
"What we have done here is something we had not done in the past. We were once considered minnows, but we are no longer minnows now.
"We achieved our objective in the first round as we played pretty well to qualify for the second round. We had just one bad game against Sri Lanka, but we played three matches and we deserved to be in the Super Eights."
Bangladesh beat debutants Bermuda and former champions India in group games to put in their best-ever performance in the World Cup since making their debut in 1999 in England.
They failed to go beyond the opening round in England where they could win just two matches. Their worst came in the next edition in South Africa where they failed to win a match.
Whatmore said he was looking forward to a better performance from his batsmen in the remaining Super Eights games.
"We need to make more runs. We were not able to score upfront in the last two matches," said the Bangladesh coach, whose side made 104 against Australia and 174 against New Zealand.
Whatmore was the coach of Sri Lanka's 1996 World Cup-winning squad in the sub-continent, but said the current Sri Lankan and Bangladeshi squads were different from the champion team.
"We needed to create match-winners (in Bangladesh), but Sri Lanka already had match-winners in 1996. That tournament was in the sub-continent," he said.
"Sri Lanka have more fast bowlers than they had in those days. They have players who play well in conditions outside the sub-continent. I think that is main reason why they have been more consistent in the past 12 months or so."