Yet another controversial decision appeared to cost Lancaster's side the chance of victory.
A fortunate second-half try from South Africa flanker Willem Alberts and three penalties and a conversion from fly-half Pat Lambie gave South Africa a 16-15 victory at Twickenham.
But with two minutes to go, and England trailing by four points, Robshaw decided to go for a penalty rather than a line-out in the corner which might have resulted in an England try.
Owen Farrell, on for Toby Flood, kicked the penalty to take England to within a point but from the restart South Africa were able to play out the game.
Against Australia last weekend Robshaw controversially decided to kick for touch and take quick taps when many thought he should have taken kicks for goal in a game which England lost 20-14.
Lancaster said: "I'm not going to talk about one individual decision over another, not immediately after a game.
"We'll sit down as a group on Monday morning when the emotion has gone out of the game and reflect on it. We discuss all the decisions. Some we get right, some we don't get right and that's part of any side's development.
"We're just disappointed to have lost the game, a game we felt we could have won."
Robshaw's controversial decision was compounded by the fact that initially he decided to kick for touch before asking the referee if he could change his mind.
Lancaster said: "The players have to make decisions on the field, as coaches we can't influence that. We back the players and support them and if we can learn from it and do better next time that's what we do.
"What we don't do is start discussing every decision in press conferences immediately after a game.
"The purpose of having a captain in a team is that he makes decisions and the players back him. That's what should happen. Was that the game-changing moment? There were lots of moments.
"We go 16-6 and you look at the team and say 'Have we got the character to take on the team second best in the world, pull yourselves back into the game and give yourself a chance of winning' and we did.
"The pleasing thing is that you cannot ever question the character of this England team at the moment, you might have done it in the past but you can't do it now. The players deserve the credit for that."
Robshaw received a measure of sympathy from South Africa head coach Heyneke Meyer.
Meyer said: "I feel for him. He's almost in a lose-lose situation. If he kicked for the corner and we contested it well he would have been (criticised). I was relieved.
"I think we were very fortunate, it could have gone either way. I thought defence of both sides was awesome. Six months ago we would have probably lost this by 20 points so I will take the one point."
South Africa captain Jean de Villiers also backed Robshaw, who had seen his side go in 9-6 down at half-time with Flood having kicked two and missed two penalties.
"Had they caught the ball from kick off they could have come into our territory, got a penalty and won the game," said De Villiers.
"You make decisions on the field and you just want the backing of your players. Unfortunately it did not work out for them. You might do it in the future and win the game.
"But we pride ourselves on our defence and we are up there with the best if not the best. We've conceded one try in three games on this tour, the attitude and commitment the guys have shown is something that cannot be coached.
"It comes from within. It is your attitude in the collision. As a captain that makes me proud."
Lancaster was delighted with the way his side matched the Springboks' physicality and insisted England, who take on new Zealand next weekend, can look ahead with confidence.
He said: "We didn't win but there is enough there from a young side to give us the confidence that we will go on to win long term.
"It's hugely disappointing, but I certainly do not go into the All Blacks game worrying that we won't get a performance next week."
Meanwhile, England defence coach Andy Farrell said: "We asked these boys to stand up this week. They were giving away a stone a man to a big side. We came out on top in a lot of areas.
"They were the better side in the first half. But they weren't in the game second half. It was never going to be a day where attacking rugby shone, both defences were always going to be on top.
"I thought there were a lot of questions asked and our boys stood up tall."
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