Robshaw was criticised for ordering Owen Farrell to kick at goal in the dying stages at Twickenham, rather than aiming for the corner and attempting to bulldoze over the line for a match-winning try.
It was a second contentious Test in a row for the Harlequins skipper, who faced opprobrium last week for choosing tap penalties instead of kickable opportunities as England tried in vain to overhaul Australia.
But Woodward said: “Robshaw is a fantastic player and a fantastic captain and the right guy to be captaining England. I expect him to be captain next week, I expect him to be captain in the Six Nations.
“This is not like club rugby. Captaining Harlequins you’re with the same players week in, week out and everyone gets used to the big decisions. When you’ve got a whole bunch of people from different clubs coming together, the art of coaching and the art of captaincy is very different, and you’ve got to find ways of making sure everyone’s on the same page very quickly.
“They weren’t on the same page with this decision and I don’t think they were last week, and this has obviously caused a big talking point, but that’s not why England lost.”
Two penalties from fly-half Toby Flood and a trio from Farrell kept England in touch with the Springboks, for whom Willem Alberts scored the only try and Pat Lambie landed three penalties and a conversion. Farrell openly questioned Robshaw’s orders for the decisive late penalty, and the flanker himself even asked referee Nigel Owens if he could reverse his call to kick at goal. Owens refused.
“It wasn’t a time for big debate,” Woodward added. “If he goes for goal, you have to do that kick within about 10 or 15 seconds. So if they’d done it very quickly, it absolutely is the right decision. Also, if I’m brutally honest, I don’t think England really looked like scoring a try against South Africa. They’ve conceded one try in three games so the chances of England scoring that try in the last two-and-a-half minutes were quite minimal.”
Flood is a doubt for England final Test of the autumn at the weekend against New Zealand, who beat Wales 33-10 in Cardiff on Saturday.