The Gunners came in for some rough-looking treatment during the Premier League encounter, particularly their striker Olivier Giroud, who appeared to be trodden on by both Glenn Whelan and fellow Stoke midfielder Charlie Adam.
Neither was punished by referee Mike Jones, but it seems the latter incident may lead to retrospective action by the Football Association.
Arsenal manager Arsene Wenger - whose side have won only once in seven visits to the Britannia Stadium in all competitions since Stoke's promotion to the top flight in 2008, and who has in the past accused the Staffordshire outfit of employing "rugby" tactics - spoke after the game about the hosts making it "very physical".
And Nzonzi said: "We know that Arsenal are a very technical team that play good football, and when you start kicking them a little bit, it gets a little bit harder for them.
"They don't like that, we know that.
"It's not a surprise they have been moaning because they have plenty of technical players."
Asked if it was up to Arsenal to be more robust, Nzonzi said: "Yes - this is how Premier League football is.
"It's really good, it's really strong.
"If they don't like that, we don't care. We will keep on doing what we can, being strong and trying to be as good as we can be on the ball."
Responding to the suggestion that it had been a physical performance from his team, Stoke boss Mark Hughes, who felt Giroud "did seem to go down quite easily on a few occasions", said: "Did you think so?
"We competed, as you'd expect us to do, and I'd be very disappointed if we didn't compete.
"I thought we got close to the ball. We didn't allow Arsenal time and space to play their football.
"But when we had possession of the ball I thought we moved it around the pitch well and had decent possession."
Saturday's contest saw Nzonzi return to the Stoke starting line-up after being absent from it for the whole of February - the first extended period like that he has had in his time with the club.
The 25-year-old Frenchman started every one of the Potters' Premier League matches from his debut for them in September 2012 up to late January, but a red card at Sunderland meant he was suspended for the 2-1 home victory over Manchester United on February 1.
He then began the next three games on the bench as Stoke drew with Southampton and Swansea before falling to a 1-0 defeat at Manchester City - a match in which he was an unused substitute.
Reports over the last few days have suggested the situation has left Nzonzi wanting a transfer.
And asked how he felt about the way things had gone over the past month, Nzonzi said: "I'm not going to lie, it hasn't been easy for me.
"But I have played many games, so I was a little bit tired, and there are also many good players at Stoke. You have to be quiet, wait your turn and keep working hard.
"It was not easy for me because every football player wants to play every game, but you cannot because there is competition and other good players who can play.
"That's how it is. That's football. You have to carry on and learn from it, and I think I have learnt from it.
"I spoke to Mark Hughes a little and he said he was being fair to all the players, and he has been.
"They did well against Man United and well after that.
"He's the manager, he makes the decisions and even if you're not really happy about that, there is nothing you can do about it other than keep on working hard."