Robshaw's decision-making has been under the microscope after he instructed Owen Farrell to kick a penalty goal when England were trailing South Africa 16-12 with just over two minutes remaining.
Farrell openly disagreed with Robshaw's decision on the field and the discussions continued down the tunnel and on into the changing room.
The week before, against Australia, Toby Flood kicked a penalty for the corner as England chased the game when Robshaw appeared ready to take the three points.
But Lancaster insisted the squad were unified in their backing of Robshaw, who had led from the front against the Springboks with a Herculean individual performance.
"Chris has done a fantastic job for us and we are 100 per cent behind him," Lancaster said.
"When I was captain, you always tend to have a debate with your fly-half because you have the decision between you - is it in your range, should we go for the corner?
"I am not concerned we have a split or a leadership dynamic that is causing me problems as a coach.
"I saw Chris on my own (when he came back into camp last night) and he was a bit flat.
"But I saw him a little bit later and he said 'I feel so much better because everyone has come up to me and said don't worry about it, we are all behind you'.
"I am proud of the team they have behaved in that regard."
New Zealand assistant coach Ian Foster pointed an imaginary gun to his head when asked how he would react if the All Blacks captain had made the same decision as Robshaw.
Robshaw believed a quickly-taken shot at goal would leave enough time for England to gather the restart and get back downfield with a chance to win the game with another penalty or drop-goal.
Had Mouritz Botha allowed South Africa's restart to land out on the full, rather than fumbling it into touch, England would have had a strong attacking position from a scrum on half-way.
The alternative would have been to go for the try by kicking for the corner and hoping England could win the lineout - no certainty against the well-drilled Springbok unit - and drive over the line.
"It was not black and white. Either decision could have won the game," Lancaster said.
"The probability of winning the game was slightly higher by going to the corner - but there was no guarantee we would have won the lineout there.
"The pressure of international sport is that decisions and execution get scrutinised but we learn and move on.
"The bottom line is we support the captain.
"The players are ultimately disappointed we (as a group) didn't make it work for Chris because he is the one who has been given the blame and it is unfair in our opinion.
"Games are never won and lost on one moment and we stand behind him."
Lancaster dismissed any suggestion that he would change his captain ahead of the All Blacks game, having appointed Robshaw as skipper for the whole QBE autumn series.
"I definitely won't be making any changes in that regard, no," Lancaster said.
The captaincy decision for the RBS 6 Nations will be taken during England's pre-tournament training camp in Leeds at the end of January.
Lancaster was anxious to highlight Robshaw's all-round contribution against the Springboks, when he led the charge as England matched South Africa's physicality.
"Chris Robshaw had a fantastic game for us," Lancaster said.
"He was the top carrier, the top tackler and he hit more breakdowns than any other player in the squad. He has done a great job for us in this series."
Robshaw will be working closely with Farrell on Saturday, with the Saracens fly-half due to start against the All Blacks after Toby Flood was sidelined with a toe ligament injury.
Gloucester's Freddie Burns is set for a place on the bench after being called up as Flood's replacement.
Lancaster believes England can handle the loss of their most experienced players - Flood was the only member of the squad with over 50 caps to his name.
"We lost a lot of caps (after the World Cup), about 600, and you think we have probably lost another 100 in (injured trio) Dylan Hartley, Tom Croft and Ben Foden," Lancaster said.
"We are not making excuses. We went toe-to-toe with two of the best sides in the world. We are hugely disappointed to lose.
"We have to learn the lessons quickly and move on. Every team grows with every game through experience and we are on that journey. The direction is the right one."
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