Well, for starters, G2 had a 3 round lead on their 3rd map, Bind (12-9), and then lost 5 straight rounds to lose the match. In comparison, TL's 3rd map Icebox had Liquid losing 5-11, which is when their comeback started and the team managed to get up 12-11 and force overtime. You may think is the same situation, but in G2's case, they lost their chance to close out the match while leading, while TL managed to force overtime after a 7-round comeback. Then, after TL found themselves losing again, they forced a 3rd overtime, while G2 didn't win a single round after being up 12-9 and lost in the 1st overtime, losing 5 straight rounds when it mattered most. So when you ask how is the way they lost different, is different in the way that TL managed to force 2 overtimes with some key clutches (GMB forced 1) and had more chances to get the W than G2 did (2 times at match point vs 1 time).
But again, no point in "what if"s. G2 qualified, Liquid didnt so that pretty much answers the original question. And I like G2 too so this is just me over-analyzing things, not dissing or anything.