Everton's Vitaliy Mykolenko branded Dzyuba a 'b****' while he and West Ham's Andriy Yarmolenko called Russian players 's********' for not speaking out against Vladimir Putin.
Dzyuba has now hit back at the criticism, taking aim at the Ukraine internationals currently in England, and also the sporting sanctions imposed on his home nation over the last week.
Russia has been banned from this year's World Cup in Qatar by FIFA, while UEFA has suspended Russian teams from all European competition, with Spartak Moscow kicked out of the Europa League last-16.
The Champions League final has been moved from St Petersburg to Paris, with Russian athletes also facing sanctions in tennis, Formula 1 and the upcoming Winter Paralympics in Beijing.
In a lengthy statement on his Instagram page, Dzyuba hit out at the criticism aimed his way, as well as the 'discrimination' against Russian athletes amid the ongoing crisis, saying he doesn't understand why they are being punished.
"Until recently, I did not want to speak on the topic of events in Ukraine," wrote the Russia captain.
"I didn't want to, not because I'm afraid, but because I'm not an expert in politics, I never got into it and didn't intend to (unlike a large number of political scientists and virologists who have recently appeared on the Internet).
"But like everyone else, I have my own opinion. Since I am being drawn to this topic from all sides, I will express it.
"I am against discrimination based on nationality. I'm not ashamed that I'm Russian. I am proud to be Russian. And I don't understand why athletes should suffer now.
"I am against double standards. Why one can do everything, but all the dogs are hanged on us.
"Why is everyone always shouting about sports outside of politics, but at the first opportunity, when it comes to Russia, this principle is completely forgotten?
"Again, war is scary. In stressful situations, people show their essence, sometimes negative. How much anger, dirt and bile has now poured out on all Russian people, regardless of their position and profession.
"Those thousands of people who write insults and threats - get in line! It is doubly strange to hear all this from people to whom Russia has given very, very much in their lives. All this only creates more negativity.
"The war will end, but human relations will remain. And it will be impossible to rewind. Remember this."
Dzyuba concluded his post by turning towards his critics from the Premier League.
"P.S. And to some colleagues in the shop who sit on their a**** in mansions in England and say nasty things: this cannot offend us, we understand everything!
"Peace and goodness to all! #I'mAPatriotOfMyCountry #SportOutPolitics"