Woodward has supported Robshaw's decision to kick the late penalty in Saturday's defeat to South Africa.
Robshaw's decision-making is under the spotlight for a second successive weekend after he instructed Owen Farrell to kick at goal when England trailed 16-12 with just over two minutes left.
A week earlier, Robshaw had decided not take the points on offer and go for the try as England chased the game against Australia.
On this occasion, Robshaw believed a quick penalty kick would allow England enough time to gather the restart, get back downfield and put themselves in a position to win the game.
Owen Farrell openly disagreed with the decision and urged Robshaw to kick for the corner - but Woodward insisted that was no time to question the captain's orders.
"It wasn't a time for big debate," Woodward told the Sportsweek programme on BBC Radio Five live.
"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.
"But if you're going to slow the ball down and debate about it then they should have gone for the lineout and given it a go."
Robshaw asked referee Nigel Owens whether he could change the call but the signal had already been made.
England would still have had a chance to win the game had Mouritz Botha allowed the South African restart to drop into touch.
Woodward backed Robshaw as England's captain into the RBS 6 Nations but urged him and coach Stuart Lancaster to ensure the squad are more unified.
"Robshaw is a fantastic player and a fantastic captain and the right guy to be captaining England," Woodward said. "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 (against Australia) and this has obviously caused a big talking point.
"But that's not why England lost the game yesterday."
England won the physical battle with South Africa but conceded a freak try to Willem Alberts and, once again, they lacked a cutting edge in attack.
Robshaw led the way as England responded from falling 16-6 down with an iron will but the red rose forwards were too often let down by poor execution from the backs.
World champions New Zealand head to Twickenham and Woodward urged Lancaster to be bold and the Rugby Football Union to show patience and support.
"New Zealand are going to score tries against England, make no bones about that, they're a quality team," Woodward said.
"I think England should pick a team that's set to score tries, and if you have that mindset then anything may actually happen.
"Everyone's got to get behind Stuart and the team now. Stuart is a rookie coach and he's got a rookie team.
"It's fairly obvious to me that when you put those two ingredients together decisions like yesterday's are going to happen at some stage.
"It's a team in development and a coach in development, but if you're going to make those appointments then you've got to back them totally and make sure you see this through."
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