South African-born Barritt had five stitches in his chin following the weekend's clash, as well as suffering a blow to his right eye.
The 25-year-old has been significant in England's campaign, acting as the cornerstone of their impressive defence, producing 60 tackles in the four Six Nations games.
"You want to step up physically," said Barritt.
"I have five stitches on my chin. At this point the looks aren't getting any better and I just have to make do with what I have got!
"If it is about helping the team it is a good feeling to come away with that and just show how hard you are willing to work for your team-mates.
"That has been one of the strengths of this side from the outset.
"Each player wants to be a leader themselves. You have guys willing to put themselves in harm's way and ultimately try and save a sticky situation."
Stuart Lancaster's side have made 759 tackles in four matches, including a record 238 in their victory over Scotland.
"It is just as important as someone making good yards or scoring a try," Barritt said.
England's defence will face a tough test at Twickenham this Saturday as they face Ireland- the Six Nations' leading try-scorers.
"The cumulative effect of someone putting their body on the line and driving opponents back is a big statement both for your side and for the opponents," Barritt said.
"It can be just as inspirational for the team and make a big statement on the opposition."