"That was a must-win game for us to stay in the tournament. I know a few players in our dressing-room who believe we can beat anybody," Mashrafe told reporters on Wednesday.
"Again, Australia is very difficult (to beat) but it's not impossible. If you have a good start you never know, so let's see."
Bangladesh's one-day international record against Australia has been poor, however, with only one win in 21 games against the defending champions who have won four of their first five games.
Australia fast bowlers Mitchell Starc and Pat Cummins have taken a combined 24 wickets in the World Cup and Mashrafe said Bangladesh will be wary of them.
"I think the Australian bowling attack has a lot of variation," Mashrafe said. "They have Pat Cummins, who can bowl with a change of pace. I think they have some good spinners. There's Nathan Lyon (and Adam) Zampa.
"So it won't be easy like the other matches but confidence is the main thing... If we took that confidence into the ground and deliver to our best, you never know."
Bangladesh will count on all-rounder Shakib Al Hasan, who is the tournament's leading scorer with 384 runs, and Mashrafe said the rest of the team must take a cue from his match-winning performances.
"Shakib is brilliant," Mashrafe added. "Hopefully, he'll keep going. The way he's playing, I think we need to support him well as a team.
"(The) bowlers have to step up a little bit with what Shakib is doing. It's going to be a good batting track. Our bowlers have to... bowl really well to restrict the Australians."
(Reporting by Shubham Kalia in Bengaluru, editing by Ed Osmond)
