Bangladesh won after successfully defending a total of 131, with left-arm spinner Nasum Ahmed claiming four for 19 as Australia were bowled out for 108 in 20 overs.
Marsh top scored for the Australians with 45 runs but conceded improvements needed to be made against Bangladesh's spin bowling.
"We all want to get better at playing spin and in these conditions there's no hiding behind the fact that it's tough," said Marsh.
"We were able to keep Bangladesh, who have played in these conditions their whole lives, to 130.
"It was tough for both teams but ultimately chasing 130, you're only ever one partnership away and we just couldn't get that tonight, so that's where the game was lost."
The defeat came in the first of five Twenty20 internationals between the teams as both nations prepare for October's Twenty20 World Cup in the United Arab Emirates and Oman.
Australia have taken a team missing the likes of David Warner and Steve Smith while captain Aaron Finch returned home with a knee injury before the end of the West Indies leg of the tour, leaving Matthew Wade to captain the side.
"We're not hiding behind the fact that we are going to face a lot of spin here, it's going to be a challenge and we've got to be up and about for it," Marsh said.
"But I think we've still got some really good players of spin here and hopefully we see that in the next few games."
