Teams play for over 6 months to gain home ice in the playoffs. And in Game 1 of the playoffs they can lose that advantage. The pressure of feeling they should win, in some places like Vancouver they have to win, and feeling the need to be perfect can be overwhelming.
It is crucial that higher seeds get off to a good start, because the road team is thinking let's take one game on the road. That can be easier mindset to take into the playoffs. The expectations are not perceived as a burden and you play free. In contrast, the home team feels the burden of expectation to win on home ice. The longer a home team is behind in Game 1 the more the fans become anxious. You can feel the tension through the television. And, if we can feel it the team can feel it!
Over the years I have talked with many elite athletes and they will often say that the first game of a playoff or tournament scenario creates a lot of nerves. How do you manage those nerves on such a big stage? Prepare your self for it. Do the hard work during the week on the ice to feel strong, and off the ice watching video and visualizing your performance in different situations so you are confident and ready. Then, when game day arrives trust in that preparation, trust in your game plan, and trust in your teammates.
During the game focus on the process - how you want to play. Physical, fast, explosive, energetic... Or, on the strategies of your role - forecheck, backcheck, drive the middle, get the puck deep... These kinds of thoughts represent positive action which a player can control and thus get in to the flow of the game. Focusing on winning and losing, the scoreboard, is not under a player's control and thus can create more feelings of doubt, a lack of focus in the moment, and erratic play (hesitating or trying to do too much).
For those home teams that lost Game 1, Philly, Anaheim, and Boston, it is important to stay focused and stick to a game plan that works. Getting down 1-0 is no reason to panic. Game 2 is obviously huge for these teams, getting down 2-0 and going on the road is not a good proposition for any team.