As noted by Mr. Dawson, the soldier was suffering from shell shock, and would, "Likely never be himself again," after Peter asked if the man was a coward. It's not really the shaken soldier's fault he acted the way he did, even if it did lead to him killing an innocent civilian. His ship was torpedoed and sank, leaving him as the only survivor. He knew the dangers of heading back to Dunkirk, and lashed out in fear because of the horrors he'd experienced.
Peter, realizing this, likely felt it was better to tell him George was alright instead of risking another emotional outburst or drastic action from the shaken soldier. In the end it didn't really matter if he knew, at least at that moment, that he'd caused George's death; nothing could change that fact, but things could easily get worse now that dozens of men were on the boat.
Mr. Dawson acts as a sort of voice of reason, likely having served in World War I, and thus familiar with the ravages of war and its affect on soldiers. He even gives Peter a nod of approval for his handling of the situation.
This scene is further expanded upon in one of the closing scenes for the film, where Peter sees the shaken soldier looking at him as they carry George's body off the boat. It's left to the viewer to decide if the shaken solder knew it was George wrapped in the sheet or not, as he'd already turned and began walking away by the time Peter looked back at him a second time.