Mashimbyi charges fell just short of the 277-run target, which would have been a record run-chase in 50-over internationals for the Proteas, with opener Tazmin Brits scoring 109.
The Proteas collapsed from 240-4 to eventually be bowled out for 261 in the final over and Mashimbyi rued his team's missed opportunity to start the series with a victory.
The head coach said: "I'm really proud of the girls. There are a lot of positives we can take out of this game. I think they showed a good fight throughout.
"Obviously it didn't go our way, which was quite unfortunate. But I think for me, as I summarised the whole game, it was a game of missed opportunities.
"For the majority of the match, we actually had control of the game, and we let it go away from us and that's when they capitalised with both bat and ball."
The tri-series in Sri Lanka is Mashimbyi's first full series in charge of the national side and he has identified areas which the team must improve before taking on the hosts on Friday.
He added: "There are so many things that we can take out. In the field, we were a bit sloppy, so that’s something we can work on.
"The nice thing about this game for me is to identify the areas that we can really improve and grow in. That's why we're never here to lose, but we're here to learn and grow."
The South African Women were made to work hard for runs as they eventually chased down 117 to defeat Bangladesh by four wickets in the Women's T20 World Cup at Lord's on Sunday.
The durable Marizanne Kapp was instrumental in the Proteas Women's victory over India in their must-win Women's T20 World Cup clash last Sunday.
The Proteas Women revived their ICC T20 World Cup campaign with a two-wicket victory over Pakistan in their Group A encounter at Edgbaston on Wednesday.
South Africa's Women's T20 World Cup campaign began with a disappointing 65-run defeat to Australia as a record chase proved beyond them.
