지다 is several unrelated verbs at once, and these lines show three. Losing a contest is the most common: 아깝게 졌지 'we lost by a hair', 깔끔하게 졌네요 'a clean loss', 이렇게 허탈하게 질 거야? 'are you really going to lose like this?'. The sun going down is another: 여름이면 해가 늦게 진대요 'they say the sun sets late in summer'. Attached to a colour word it means turning that colour (뻘게지다 'go red'). One line is a different verb altogether, 짓다 'build'.