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Australia will play Test cricket in Bangladesh for the first time since 2006 when the first of two Tests gets underway in Mirpur on Sunday.
The Tigers, who ranked a lowly ninth in the world in the longest format, have only won nine of 100 Tests that they have played since the ICC gave them Full-Member status in 2000.
However, Shakib reveals a change of mind-set in recent season has allowed them to produce better results, especially at home.
Shakib told The Guardian: "Previously the mind-set was to draw against big teams - try to play five days, make a draw.
"But we never used to get the result. Then we started thinking, 'Let's try to win - let's try to play and win the game'.
"It's the mind-set that changed, and that made us believe that we can win."
Home form in the ODI format has also helped the Asian nation gain some confidence with series victories over Pakistan, India, and South Africa in the 50-over format in recent seasons.
And those results have instilled self-belief in Test whites with the Tigers drawing a two-Test series against England last year followed by their first win in Sri Lanka in March.
Shakib continued: "It's been a long journey. It's been incredible. I don't think many people thought - even in Bangladesh - that we can come this far.
"We knew that we have this ability, and we needed that belief, and we can only get this belief by winning matches.
"But there is no shortage of self-belief at this moment - Now we feel that we are very much unbeatable at home - doesn't matter who we are playing against."
