During their 10-wicket reverse in their second round opener against world champions Australia, Bangladesh collapsed to 65 for five on the way to a total of 104 for six in a match reduced by rain to 22 overs per side.
However, against New Zealand, Bangladesh enjoyed an opening stand of 55
Tamim Iqbal made 29 and Javed Omar, in for the out-of-form Shahriar Nafees, 22. But on a good pitch their runs came at a sedate pace of under four an over.
And after they exited, Bangladesh collapsed to 174 all out at the Sir Vivian Richards Stadium.
Looking ahead to Saturday's match against South Africa, another major power, Bashar said his largely youthful side needed to strike a balance between their natural attacking instincts and excessive caution.
"The team plan is not to lose too many early wickets to the new ball," Bashar told reporters after New Zealand had won with more than 20 overs to spare here Monday.
"It means we need to be careful, but I think maybe we were a little bit too careful.
"We need to do something in between - either we're hitting too much, or blocking too much."
All four of Bangladesh's top order made it into the 20s against the Black Caps but none of them were able to press on and Bashar added: "Our top four batsmen got a start and didn't finish it; if one of them could bat for 30 to 40 overs we can put some good runs on the board.
"It is a little bit frustrating - but I still believe in my players. They have shown they have the talent and the capabilities to get top runs," said the Bangladesh skipper, whose side beat New Zealand in a warm-up match before enjoying a group victory against India.
"We've had a pretty difficult first two matches in the Super Eights. But we still have four to go, and our goal is not to repeat the mistakes we have made so far. But we still believe we can come back from here, and come back strongly for the next game."
Bashar's leadership skills off the field, backed up by input from experienced coach Dav Whatmore, who guided Sri Lanka to the 1996 World Cup title, will have to come to the fore during the next few days as Bangladesh look to rebuild their morale.
"We need a good show in our next game to get our confidence back up - because we are a little bit down," Bashar explained.
Having now played two of the leading contenders for the World Cup, Bashar said there was little to choose between them.
"They are very different teams, and both have a good chance (of winning the World Cup). New Zealand play with a lot of all-rounders and bat down the order, Australia have top-order batsmen who score big runs.
"Whoever wins the World Cup this time will have to work very hard."