But Welsh referee Nigel Owens told him he had already made his call and it could not be altered.
Boos reverberated round Twickenham as England spurned the chance of a glorious finale.
Blasted for not kicking their penalties against Australia last week, England had gone from chance-takers to no-risk rugby.
Farrell could initially be heard expressing his desire to kick for touch on the ref link.
But Robshaw defended his decision after the match and Farrell – a replacement for Toby Flood who had an X-ray on a suspected broken toe – insisted that he backed the captain.
Robshaw said: “The decision comes down to me and I thought potentially we had time to get the points and get back down there and put ourselves within drop-goal or penalty range but it didn’t come off.
“It’s one of those where if we’d won it would have been the right call but, unfortunately, we didn’t.
“We discussed it but I make the calls and, at the end of the day, it’s on me. We’d tried to drive them a couple of times and didn’t have much luck so that was another thing that came into mind.”
He admitted that Farrell expressed a preference to go for touch but maintained: “I’m the one who makes that call. It’s on me.”
But Robshaw denied he was under pressure after England failed to take the kicks which could have beaten Australia.
“Not at all. You need to be big enough to go out there and make your own decisions – but two weeks on the bounce it didn’t quite work for us.”
Farrell said: “It wasn’t my decision. We backed him and we still thought we could win the game.
“He might not have known I was over the other side of the field and it was going to take so long for me to get over there.
“The (kicking) tee was already on by the time I got over there.”
There were only 70 seconds left when the Springboks resumed and it was game over when England’s replacement lock Mouritz Botha fumbled the restart kick into touch.
England head coach Stuart Lancaster refused to criticise his skipper.
“I am not going to comment on individual decisions,” he said.
But Lancaster was happier with England’s performance than he was after the 20-14 defeat by Australia.
He said: “It was a big step up from the Australia game. We are going to bottle the frustration and take it on against the All Blacks next weekend.”
Robshaw added: “I think were are improving. We were a lot smarter with our game today than last week.
“We are creating chances and it’s now going that extra five or ten per cent and finishing them off. It will come.”
South Africa coach Heyneke Meyer said: “I feel for him (Robshaw) in this situation. If he’d kicked for the corner, we’d have contested well and everyone would have said he’d had time for the goal and then enough time after that.
“It was a hard-fought battle which could have gone either way. If one more kick had gone over from them it was suddenly a different score.
“The defensive play of both sides was awesome.”
MIKE SINCLAIR