Answer #2: Mismatch

The Penguins and the Senators each finished the regular season with 105 points. Only two teams scored more goals than the Penguins did this season, and Ottawa was one of those two teams. Ottawa was also one of the rare teams, like Pittsburgh, that could roll four lines. Perhaps more than just rolling four lines, the Senators rolled four lines composed mostly of players who'd long ago learned how you have to play in the NHL postseason.

If the standings had been seeding differently, rather than giving Atlanta the third seed for winning their division, the Pittsburgh flaws that the Senators exposed might not have been revealed until the second round of the playoffs. And, by that point in time, perhaps the Penguins, who might have experienced playoff hockey by beating a different team despite a few hiccups that surely would have come, would have been slightly better equipped to deal with Ottawa's deeper, more experienced team.

Plain and simple, the match against the Senators was a mismatch for Pittsburgh. The Senators' team was designed to exploit every one of Pittsburgh's weaknesses. Of other Eastern Conference teams, perhaps only Buffalo could have so starkly revealed the Penguins' inexperience and need for still more depth in various areas.

While I still believing inexperience to be the primary culprit in the Pens' first round loss to the Senators, and as a part of inexperience I am including the fact that every single one of Pittsburgh's core players is not yet in his prime, the fact of the matter is that the Senators were, at least this season, the superior team.

That being said, it sucked that the Pens had to face a clearly superior team in the first round of the playoffs. But, as they say, it's a learning experience, right?

(Present Day Reflection: As it turns out, the Senators were also a mismatch for the Atlantic-Division winning New Jersey Devils and the President Trophy winning Buffalo Sabres. The Penguins are not in "bad" company. Perhaps it's better that Pittsburgh's youngsters were beaten by the eventual Eastern Conference championships--because such a loss clearly revealed just what the Pens need in order to become a team that can beat Ottawa.
On the other hand, it's something of a bitter pill to swallow. All the "if's"--despite how thoroughly Ottawa beat Pittsburgh--perhaps showed that the Pens, while far away from being the Eastern Conference champs, aren't that far away--certainly no further away than the other teams considered the "elite" of the Eastern Conference.
Yet, the fact of the matter is, being eliminated is being far away, no matter how ostensibly close you are, you've still got a long way to go.)