The Rangers midfielder appeared to mock his opposite number as Steven Gerrard's side claimed victory at Ibrox last month.
Arfield was praised for keeping Brown and company quiet during Rangers' 1-0 Old Firm win at Ibrox last month.
And the pair's battle was made all the more spicy when Arfield appeared to mock Brown by imitating the Celtic captain's trademark arms-aloft celebration after the latter was booked in the second half.
Asked about that particular incident from Rangers' winter training camp in Tenerife this week, the 30-year-old replied: "[It was] spur of the moment, it’s just one of those things." On whether or not Brown was "alright with it", he added: "I think so, I think so. I hope so."
Arfield later explained how Rangers adopted a fresh approach against Brendan Rodgers' side this time around.
"I’ve watched the games from afar and in my opinion, nobody’s really challenged him [Brown] - got up close to him," he said. "We were guilty of doing it at Parkhead - we never got up against Celtic and really went after them.
"This one was completely different with the formation we played, and a willingness to get after Celtic allowed me to go ahead and express my game."
The result leaves the Scottish Premiership title race finely poised ahead of the run-in, with Rangers now level on points with leaders Celtic - albeit having played a game more than their rivals.
Both clubs have already been busy in the January transfer market, with Jermain Defoe and Steven Davis joining Rangers, and Oliver Burke and Timothy Weah heading to Celtic.
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