Zimbabwe needed five runs to win as fast bowler Mashrafe Mortaza ran in to bowl the final delivery of the Harare match.
Brendan Taylor smashed the full toss over the mid-wicket boundary for six to clinch Zimbabwe's two-wicket win.
''These things happen in cricket,'' Mashud told Reuters.
''We did our best, and while it was disappointing to lose like that there's no shame in losing off the last ball.
''In any case, what happened yesterday is gone -- we have to keep our minds focused on the rest of the series.'' The result earned Zimbabwe a 2-1 lead in the five-match series, and Bangladesh will attempt to level it when the teams meet in Harare tomorrow.
''We have two matches to go, and we know we have to win both of them to win the series,'' Mashud said.
''We are confident and motivated that we can do so.'' Mashud, who took over the captaincy when tour captain Habibul Bashar broke his thumb while fielding in the slips in the second match of the series on Sunday, said he was satisfied with his team's performance in two of cricket's three core disciplines.
''Our bowling and batting is in good shape, but we need to work on our fielding,'' he said. ''It is improving every day, but we need to tighten up the fielding if we want to play good cricket more consistently.'' The last match of the series will be played in Harare on Sunday.
Zimbabwe: Prosper Utseya (captain), Chamu Chibhabha, Elton Chigumbura, Terrence Duffin, Ryan Higgins, Anthony Ireland, Friday Kasteni, Blessing Mahwire, Hamilton Masakadza, Stuart Matsikenyeri, Tafadzwa Mufambisi, Tawanda Mupariwa, Ed Rainsford, Piet Rinke, Vusi Sibanda, Gregory Strydom, Brendan Taylor.
Bangladesh: Khaled Mashud (captain), Aftab Ahmed, Alok Kopali, Farhad Reza, Javed Omar, Mashrafe Mortaza, Mohammad Ashraful, Mohammad Rafique, Mushfiqur Rahim, Rajin Saleh, Saqibul Hasan, Shahadat Hossain, Shahriar Nafees, Syed Rasel.