How did Stalin justify his actions in Eastern Europe to the Western allies?
In many ways, he never really had to. If you look at the way he interacted with them at meetings, Stalin was constantly pushing to see what he could and couldn't get away with. Particularly towards the end of the war, he was no longer nearly as dependent on the West for supplies, so he knew that they didn't want to get in too much of a shoving match.
Of course the Allies were also somewhat unwilling to push back too hard because the Russians had absorbed millions of casualties to destroy the German army, saving the rest of the Allies from that incredibly daunting task. Because of this, they felt that he was entitled to some leeway.
Of course FDR, later Truman, and Churchill knew that Stalin was pushing to gain as much territory as possible, but rather than confront him too strongly about those actions, they tried to push east as quickly as they could to make sure that he didn't overrun too much of Europe.
The previous thoughts were quite accurate in that Stalin never really had to justify his thoughts to anyone. There were objections to what he was doing, but in the end, Stalin's desire to create a series of buffer states that would be able to prevent another Western attack of Russia became the guiding premise behind his actions. This desire to consolidate control and bolster his own standing amongst the nations of Europe became the primary focus of the Soviet leader. His Western Allies began to understand quite soon after the conflict's resolution that Stalin sought to go his own way and given his strength at negotiations, there was little in way of justification and explanation needed.