Oilers didn't create enough in the first two periods, Panthers controlled it. Until the Panthers went into the defensive shell in the third, Oilers weren't good enough. No guarantees they get back
Exactly. That PP opportunity the Oilers had, where the Panthers D broke his stick? You can't let a chance like that get away from you in a Cup deciding game. And the Oilers didn't cash in. They weren't creating enough all night, with the third period largely due to score effects.
The SN crew were raging homers especially in the second intermission, but in the first intermission one of them did point out that the Oilers were playing a very safe looking game as opposed to trying to push and drive the play. They never followed up on that, and they were slow to give the Panthers the credit they were due for not giving the Oilers an inch of open ice to work with all game. The score may have been just 2-1 but that was a pretty decisive Panther win. The Oilers never had control of the game, and their best players on paper were not their best players on the ice. Not a winning formula for them. For anyone, really.
And yes, no guarantees the Oilers can run it back. Panthers are the first team to pull it off since the 08/09 Penguins, and they were the first since the 83/84 Oilers IIRC, though if you expand the "run it back" criteria you can come up with some others such as the 19/20 Bolts, 95/97 Wings. Still, it's the exception, not the rule.