Bangladesh have succeeded where mighty Pakistan and India both failed by reaching the second round and were taking on world champions Australia in the first of their six Super Eights games here on Saturday.
"The team has got a lot of performers these days. At the moment we are beating some top sides," said Bashar.
"We beat New Zealand in a warm-up game and we had a good win against India (in the first round). 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.
"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.
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."