I think that the Celtics core was too young [with the exception of Horford, who obviously is a playoff veteran] and couldn't quite get over the hump due to collective inexperience. Losing game 7 to a Lebron led Cavs team was predictable, even though they were at home.
However, advancing to game 7 of the conference finals, dealing with the pressure associated with playoff basketball, etc. makes those young players grizzled playoff veterans now. I wouldn't expect them to be as "tight" in an elimination game this time around. Several of those players were getting their first taste of playoff basketball.
Also, they were awful on the road in the playoffs last year -- which makes it even more amazing that they got to game 7 of the conference finals. Another sign of inexperience that will need to change, and probably will now that they've been through the wars a little bit.