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."
Tebogo Macheke has earned her first call-up to the Proteas Women's squad for the upcoming five-match T20I series against India, with the national side also making changes to the coaching staff.
Proteas Women's seamer Ayabonga Khaka has jumped to 12th in the latest ICC world bowling ranking after an outstanding ODI series in New Zealand where she was the leading wicket-taker.
New Zealand clinched a 2-1 series victory over South Africa with a 66-run win in the final women's ODI in Wellington on Saturday, bringing the tour to a disappointing close for the visitors.
Amelia Kerr put on a show as she guided New Zealand Women to a record run chase of 346 for a narrow two-wicket win in the second ODI in Wellington on Wednesday.
