In secular society, the new year is frequently ushered in with levity and drinking, whereas in Judaism, the beginning of a new year is a solemn occasion preceded by a month of soul-searching and teshuvah.
The first day of the new year is an undeniable indication that another year of life has receded into the past. If one looks back on the bygone year and sees nothing of real achievement, one is likely to become quite dejected. People who must face the realization that a year of their lives has essentially been wasted cannot celebrate the arrival of a new year unless they drink to the point they become oblivious to this reality. Only then can they exclaim, "Happy New Year!"
In Judaism we prepare for the advent of a new year with reflection and teshuvah. Whereas making a personal inventory should be done all year long, it takes on special significance during the month before Rosh Hashanah. A comprehensive reflection on the events of the past year enables us to see what we have done right, so that we may enhance our efforts in those directions, and to see where we have gone wrong, so that we can avoid repeating the same mistakes.
Such an analysis enables us to use the lessons of the bygone year to better ourselves in the coming one.
This is why we do not drink or behave raucously on Rosh Hashanah. If the past year has value as a lesson for the future, there is no need to drown it from our consciousness.