In the group stages, Bangladesh's five-wicket defeat of India effectively ended the 1983 champions' participation in the tournament.
But Bangladesh face their toughest test of the competition so far here Saturday when, in their Super Eight opener, they take on world champions Australia, who have swept all before them as they chase a third straight World Cup title.
However, Bangladesh head into the match at the Sir Vivian Richards Stadium knowing that two years ago they caused the greatest upset in one-day international cricket history with a five-wicket defeat of Australia.
"We had a team talk and I heard from all the boys they think they are not finished yet. They want to do something in the Super Eights as well," said Bashar.
Bashar, one of six survivors in the Bangladesh side from that memorable match in Cardiff, including century-maker Mohammad Ashraful, believes the team he leads now is better equipped even though they have since lost five one-dayers against Ricky Ponting's men.
Asked if Bangladesh could beat Australia again, Bashar replied: "I think so. I think if we can do it, it will not be a great surprise.
"It's going to be very tough but we believe it is not an impossible task," added batsman Bashar, whose team's triumph in the Welsh capital remains their only victory in 12 one-dayers against Australia.
"The team has got a lot of performers these days. At the moment we are beating some top guns.
"We beat New Zealand in a warm-up game and we had a good win against India. We now strongly believe that if we play together, we can beat anyone."
Bashar, 34, is leading one of the youngest teams at this World Cup. For example, opening batsman Tamim Iqbal, who made 51 against India, only turned 18 earlier this month.
And their captain said Bangladesh's lack of experience has given the side a fearlessness they might not otherwise have.
"Sometimes when you play a team like India, if you think too much, plan too much, it is not going to happen. It's better to go out there with a positive mind and play whatever you can. Don't think too much, that's what we're planning to do."
And he said he'd be happy to see the likes of Iqbal going down the pitch to take on Australia fast bowler Glenn McGrath. "I hope so. That's what we're banking on."
Looking ahead, Bashar said there was less pressure now on Bangladesh than in the first round where, after losing to fellow qualifiers Sri Lanka following their win against India, they had to beat minnows Bermuda to secure their place in the Super Eights.
"Everyone has been saying the Super Eights will be tougher but I believe the first round was tougher for us because every game we played was like our last game. But in the Super Eights we will have a chance to play six games."
Bangladesh are not the only team to have caused an upset at this World Cup. Ireland's defeat of Pakistan sent the 1992 winners crashing out of the tournament and Bashar said such results were good for cricket as a whole.
"The performances of Ireland an Bangladesh show that cricket is getting bigger and that teams who are not at the top of the rankings can still do something in this competition."