Was Apollo saying no to the Russian or to Rocky.

Hi.

Before the second round starts, Rocky is trying to persuade Apollo to retire from the match after being badly beaten up by Drago in the first round. However, Apollo insists that the match goes on and instructs Rocky not to stop the fight no matter what happens.
As Apollo is getting even more badly beaten up in the second round, Rocky raises the towel to throw into the ring (which would signal to the referee to stop the fight and therefore award the win to Drago). Apollo sees Rocky raising the towel, and says "No!" to Rocky, as Apollo would rather lose by knock-out for the sake of his reputation than lose by retirement.

Of course, Apollo is then tragically killed by Drago. Rocky then becomes guilt-ridden that he didn't save his best friend's life by throwing in the towel, and vows to avenge his death by agreeing to a match against Drago in Russia.

I don't think he would have been saying it to Rocky. With the noise of the crowd and the fact that Apollo was clear on the other side of the ring I doubt Rocky would have heard him say anything. And how could Apollo have noticed that Rocky was holding the towel and getting ready to throw it when he was being beaten senseless by Drago at the time? He was probably barely even conscious at that point.