FIFA Women's World Cup
The defending champions were the overwhelming favourites going into the Group E tie at Eden Park but were instead made to work hard for a 3-0 win.
Sophia Smith scored twice with Lindsey Horan netting the third as the United States kicked off their bid for a fifth world title.
While there was no doubting the superiority of the Americans, Mai said he was proud with how Vietnam had stuck to their gameplan.
"We lost in terms of capability but we did our best against a very good team who I believe are among the favourites to win the title," said Mai.
"As I said on Friday, we knew it was going to be very difficult to play aginst the defending champions. I said we could lose quality wise but not by spirit and today we showed we could play."
The final statistics were overwhelmingly in the United States' favour, with seven of their 28 shots on target compared to none for Vietnam.
"We tried to attack by pressing them but as you know, the level of capability is very different between the two sides.
"We tried to limit their aerial attacks, we tried to be tactical, skillful and I think we succeeded to a certain extent."
A resilient defensive display frustrated the United States and Mai applauded his players for maintaining their focus.
"We tried to prepare well, the players covered each other and the goalkeeper did very well as she not only saved a penalty but made several other key stops.
"However, there were certain areas that we could have done better in and we will work on them before our next match (against Portugal on Thursday).
Photos: FIFA via Getty Images
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