Da Gama's side wasted numerous chances as they succumbed to Robert Skov's 69th minute strike at Mane Garrincha Stadium in Brasilia on Sunday.
The national team, who held hosts Brazil to a goalless draw in their tournament opener, will conclude their Group A campaign against Iraq in Sao Paulo on Wednesday (03h00 kick-off SA time on Thursday).
South Africa are bottom of the pool with a point - one point behind Iraq and Brazil, and three shy of Denmark. The top two nations will advance to the last-eight of the global showpiece.
“To a certain extent luck was not on our side. However, we let ourselves down – no two ways about it. We created so many chances but could not convert any of them. At some point we had the edge, we were on top of Denmark. (Keagan) Dolly and (Gift) Motupa were unfortunate not to score after their shots hit the woodwork,” Da Gama said.
“I also think players need to raise their hands when called to represent their country. There were times when I felt that there was no sense of urgency from some individuals. In some situations they should have been brave and take players on, but they didn’t.”
Da Gama said Mothubi Mvala's suspension forced him to make tactical changes against the Scandinavians.
“Following Mothobi Mvala’s red card against Brazil, we had to move things around. We pushed Motupa up to attack and played Kwanda Mngonyama and Deolin Mekoa in holding midfield but this didn’t work for us. Maybe we should have tried a different combination.
“A win would have eased the pressure of progressing to the next round after all four teams were tied on a point each from the first matches. We really let it slip against Denmark, and now we have made it tougher for ourselves, but not all is lost yet. We still have the final group stages match which will determine our fate in the competition. We know it won’t be easy but we are still confident we will make it to the quarter-finals.”