Drago HAD to knock Rocky out in the last round. Yes he probably would have won in an unanimous decision but he had already lost the respect of the Soviet leadership by allowing this tiny American win the respect and hearts of Russian people. By not knocking Rocky out, and especially if he avoided Rocky in the last round, he would come out of that fight in a lower status than he was before it, despite having won. He would have won the battle, but lost the war.
Drago failed after the 2nd round. Everything was on him having Rocky broke by the end of the first so he could go for the KO and the statement win. Ivan realized he was screwed once they went to the corner and he mentioned Rocko was "made of Iron," he knew he wouldn't be a bum to push around. Then Rock hit him with that hook and cut him open.. he was done for after that his rep was ruined and he never would have been the same.
It went from a boxing match to a fight and war of geo political importance and Drago had no way to handle it. Rocky represented a whole other style and worldview.. Ivan was broke as to fight it. He lost his mind and choked out his promoter which killed his rep too. The whole "I do it for me," rant was huge. Then it became a fight for his honor and the win; enough of an ego mistake to help Rocky get momentum enough to put him down for good. Ivan lost the same way Apollo did ironically.. if both had stayed away from Rocky they woulda won on points but their hubris brought them down.