The flanker opted for Owen Farrell to kick at goal when England were only trailing 16-12 to the Boks with a few minutes left, and failed to score from the restart.
“I definitely won’t be making any changes in that regard. The most important thing is we backed the captain and the players are 100 per cent behind him,” said Lancaster, who confirmed fly-half Toby Flood will miss Saturday’s clash with New Zealand due to a toe injury.
The incident followed criticism of Robshaw’s decision to forgo kickable penalties in the 20-14 loss to Australia last week.
“Games are never won on one decision. There were lots of little decisions that put us in that position and meant we were chasing the game,” said Lancaster,
“In hindsight we should’ve maybe gone for the corner but what disappoints us as a group is we didn’t make it work for Chris.”
Owen Farrell is set to replace Flood at fly-half against the All Blacks, with uncapped Freddie Burns on the bench as cover.