An entertaining and end-to-end match in Warsaw, which was marred by more than 100 arrests for violent clashes between people in the city earlier on Tuesday, ended in a 1-1 draw.
Russia had taken the lead when rising star Alan Dzagoev scored his third goal of the summer's finals in the first half.
But Poland, who had nine shots on target, equalised in spectacular style in the second half through captain Jakub Blaszczykowski.
Russia remain on course for the quarter-finals but Arshavin was disappointed at surrendering the lead as he said: "We started well and took the lead.
"But, after the break, we played too loosely allowing Poland to reply on dangerous counter-attacks."
Russia's Dutch coach, Dick Advocaat, praised Poland for their performance and added he was happy with the point.
"Poland played very well tonight, being under the risk of losing the chance to win a place in the last eight if they lost," he said.
"Meanwhile, we allowed them to create too many chances in attack.
"That means we still need to strengthen our defence. We also played well and scored before the break and had many chances in the second.
"But we missed them all. In general, I would say the draw is a good result for us."
Poland coach Franciszek Smuda declared himself satisfied with his players and believes his young side will only improve.
"We are a young side, and we are going to get ever better," said Smuda.
"I am above all happy with the players because they played to the game-plan from the first to last minute."
The result leaves Russia top of the group with four points but Poland can still advance to the knockout stage if they beat Czech Republic in their final game.
Blaszczykowski added: "We're still in the tournament, so with this point a win in our final match puts us into the knockout stage."
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