Sokratis was adjudged to have fouled Salah for a first half penalty, which was converted by the Egypt international to put the Reds into a 4-1 lead.
The Greece international was fuming at what he felt was a dive by the Liverpool forward after what appeared to only be minimal contact between the two players.
As both sets of players headed down the tunnel for the 15-minute interval, Sokratis continued to lay into Salah, disparaging remarks which Van Dijk took exception to.
"I saw that he went to Mo and was saying that he dived," the Dutchman, who had to be kept apart from the Gunners defender by team-mates and police, told reporters.
"He was attacking him a bit, but I wanted to say he didn’t dive.
"Obviously everyone came around us and it looked like we were fighting or something, but we weren’t.
"I just wanted to talk to him. But that happens in football and we move on.
"I’m protecting my team-mates and that’s normal, that’s how everyone should react and that’s what we all need to do, to back each other. That’s what I definitely do."
Manchester City's win over 10-man Southampton means Liverpool's lead ahead of their meeting on January 3 stands at seven points following a contrasting festive period for the leading contenders for the Premier League title.
After having previously ignored the looming trip to Pep Guardiola's men, Van Dijk now says all of Liverpool's focus is on the clash with the reigning champions.
He added: "We were almost perfect, we conceded the goal and that was the only thing. But it was an important win.
"After this we can now focus on the City game. Before we didn’t do that.
"Arsenal had been playing pretty well this season so we had to stay focused on them, not think about City.
"We have finished 2018 now pretty well and hopefully we can keep that going.
"City is a game that we want to win. It will be very hard, very tough, but for them as well.
"It’s going be a good match, but it is not a decisive game or something like that. We are not going to treat it different to any other.
"We will be prepared for a very tough game."