Former Australia batsman Whatmore was dismayed to see a succession of Bangladesh top order batsmen try and fail to hit Glenn McGrath off his length during their 10-wicket defeat by the reigning world champions on Saturday.
McGrath, who during the course of the match broke Pakistan great Wasim Akram's record of 55 World Cup wickets, said Bangladesh's approach had much to do with the fact rain had reduced the game to 22 overs per side.
But Whatmore insisted too many of his batsmen had played a part in their own downfall by being overly aggressive early on and so helping McGrath to a haul of three for 16 in five overs.
"I wasn't very happy to see that. He's got the best economy rate of all their bowlers. The boys knew that yet they still wanted to hit him. That's the frustrating part. You can see the talent in our kids, you tell them he's not easy to hit yet they still try to hit him," Whatmore said.
"We've got to have a little bit more discipline, apply logic and then we'll do better.
"The boys have got the ability, but a rush of blood here and a rush of blood there and it's so frustrating."
Bangladesh beat New Zealand by two wickets in a World Cup warm-up match last month.
But since that reverse the Black Caps have been in fine form and Whatmore believes they could be one of the sides capable of stopping Australia from winning a third straight World Cup title.
"They are a good solid team in any conditions and they'll be good opposition on Monday. They are strong all over, a very good fielding team and they bat deep with allrounders.
"They have a lot of flexibility and are difficult to bowl out," added Whatmore, Sri Lanka's coach when they won the World Cup in 1996.
Two years ago Bangladesh caused the greatest upset in one-day international cricket history when they defeated Australia by five wickets in Cardiff.
However, Australia captain Ricky Ponting believes that Bangladesh, who beat India at this World Cup, are a better side now than they were then.
"They've come a long way since I first started playing against them and the exciting thing about them is that they've got a few 17, 18, 19-year-old kids in their side which is exciting for any team to have."
And New Zealand skipper Stephen Fleming insisted there was no way his side would be under-estimating Bangladesh after their recent experience.
"They turned us over in the warm-up game and they've been competitive through the World Cup and if conditions are right they can be quite a handful," he said.
"The danger is complacency, under-estimating what they can do. I think it's a blessing in disguise that we know what they can do.
"They bowl a different length, they are able to exploit fresher conditions because they bowl fuller. They provide different challenges, challenges you don't get facing your own bowlers in the nets - so that's where the adjustment comes from."
Bangladesh have a fitness doubt over pace bowler Tapash Baisya who had to leave the field with what appeared to be a foot injury during his third over against Australia.
New Zealand are set to field largely the same team that beat West Indies by seven wickets on Thursday although Mark Gillespie, yet to play in the World Cup because of a shoulder problem, could replace fellow pace bowler James Franklin.