Speaking to reporters at the Great Barrier Reef Arena in Mackay, Carey said he would like to see the two teams play more Test cricket in the future.
Bangladesh returned to Australia for a Test series for the first time in 23 years, with the two-match contest ending 1-1.
The Tigers stunned the world's No. 1-ranked Test side by winning the Darwin opener by nine wickets, before Australia bounced back in Mackay with an innings-and-51-run victory inside two days to level the series.
The two teams had already faced each other across all three formats earlier this year, when Australia toured Bangladesh for three ODIs and three T20Is. Bangladesh won the ODI series, while Australia claimed the T20I series.
Reflecting on the recent contests, Carey praised the competitive nature of the rivalry.
“It was an exciting series, played in a great sporting spirit. Over the past few months, we’ve had some really good contests against Bangladesh across ODI and Test cricket.”
Carey also expressed his desire to see Bangladesh return to Australia more regularly for Test cricket.
“I think we’ll see Bangladesh a lot more in Test cricket. We want to play more series against them. It’s also been really nice catching up and having a chat with them after the matches.”
Bangladesh's previous Test tour of Australia came in 2003, with Cricket Australia’s reluctance to host the Tigers contributing to the long gap between the two teams' Test meetings.
