Arsenal saw off determined Championship outfit Plymouth 3-1 at Emirates Stadium to book a place in the fourth round of the FA Cup.
"We did the job in a serious way and had we not been focused and completely up for it, we would not have gone through today," Gunners boss Arsene Wenger said.
"I give credit to my team for doing the job seriously, and also to Plymouth who had a great game as well.
"I was surprised how well they were organised and how strong they were in every challenge. They did not die physically and were always dangerous on set plays.
"The gap between the Championship and the Premiership has been reduced and looking at the FA Cup results today, you could see that."
Van Persie, 25, was given the armband by Wenger in mark of his all-round improvement.
"Robin has always been interested in team affairs and wants to help sort things out," said Wenger
"He is a big example of how well you can have an evolution, when you consider when he came he and who he is today."