Itoje was picked up on the referee's microphone shouting at Smith "don't argue with me, take the three" as the pair and other players discussed whether to kick for the corner or for goal from a penalty early in the second half.
"I was unaware that a lot has been made of it," Smith told Rugby Union Weekly.
"Maro's a great mate of mine. We've got a good relationship and I think it's the same way you speak to a good mate or a brother.
"Always around penalties you want to give your opinion, but at the end of the day the captain makes the final decision.
"He was well within his rights to put his foot down and tell us what we're doing."
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The pair's exchange has become a running in-camp gag in the build-up to England's final-round meeting with France on Saturday, with Smith, 5ft 11in, 13st 13lb and 15 caps, joking that he and Itoje, 6ft 5in, 18st 8lb, 101 caps, would settle a difference of opinion physically, rather than verbally, next time.
"I thought it was funny," said Smith. "Me and Maro have been joking about it this week and I told him if he shouts at me like that again, I'm going to punch him!"
Itoje, usually a composed presence on and off the pitch, insisted his raised voice was not a lost temper.
"I didn't really lose it!" he laughed. "You don't often see me with a mic. I'm not always mic'd up but maybe I'm portraying a false image.
"Fin is my guy. The way I try to do things is to hear what my key decision-makers think of what is going on, and whoever plays 10 will obviously have an important role in that.
"It's a good thing that people in the team feel they can express a view, and in sport, if anything, that's the most kosher of fallouts that the world has ever seen.
"We have had far more blunt conversations between ourselves and other team-mates."
England have had cause for frank discussions during this Six Nations after three successive defeats left their title aspirations in tatters.
Another against France would mean England finish with a return of one win from a Six Nations campaign for the first time since the tournament expanded in 2000.
England have only lost four games in a single edition of the 143-year-old championship twice previously - in 1972 and 1976.
Smith, who made his first England start in the victory over France last year at the beginning of a 12-match winning streak, is in an unfamiliar position.
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For the 23-year-old, who won the Premiership title with Northampton in 2024 and reached the Investec Champions Cup final in 2025, was also picked for the British and Irish Lions squad which toured Australia last summer.
"For a young guy that's not had too much adversity in an England shirt so far, I think it's been an interesting week for me to handle," said Smith.
"I've had the excitement of being back in the team for the first time in a little while and then obviously a really disappointing result over in Rome.
"It's a weird way to describe it, but it's almost like grief when you lose a game like that.
"You really hurt from it, and trying to park those emotions and then getting yourself into a position to be really excited for a massive game coming up this weekend has been a good one for the group actually.
"I think we will have grown a lot from it and learned a lot about ourselves."
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