This is a base breaker kind of situation - Player reaction pretty much depends on asking the question how connected are you to the asari? If, for example, Liara is your romance and you love the asari, then seeing their homeworld fall and burn is devastating. If, though, you're not that fond of Liara and think the asari are haughty and arrogant, then at best, it's a tragic event that's being repeated all over the galaxy, and at worst, it's karma at its finest, given the asari's refusal to come to the table until the Reapers are already on their doorstep. (Full disclosure, I do slant more towards the second interpretation than the first.)
However, the plot assumes the former situation to be more likely than the latter, ignoring the player's perspective. Shepard is broken, and, based on the dialogue, it's just as if not more about Thessia's fall than the loss of the data. (Shepard can say "Thessia's fallen and that's on me.") To some, Shepard hitting the breaking point doesn't feel earned based on the way that things play out - losing the data is demanded by the plot, and it's done in a way that feels cheap, when you can in gameplay have Kai Leng on the ropes, and then he just walks over Shepard when the cutscene kicks in. And again, the player connection comes into play - if I don't particularly care about Thessia and the asari, then seeing it burn really doesn't have the same effect as watching Earth burn, or watching the Normandy be destroyed. Part of the flaw in this sequence, I think, is that there's no opportunity for the player to forge a connection to Thessia - it's the first time we've been there, and the Reapers are already reaping, so we don't get the time to stop and understand why we should care about Thessia.
I get the intention - Tuchanka, the coup, then Rannoch, not to mention Sovereign and Saren and the Suicide Mission from the previous games, set Shepard up as a heroic figure who could always win against impossible odds, and then loses this round, but the way it's executed is... spotty at best. It's not a feeling of 'I lost the data' but 'the plot says that I lost the data.'