Even though it is human nature to assign blame, this is rarely seen to be justified, especially in cases as large as the tragedy of the Titanic. The lessons that needed to be learned where the end result of systemic problems in the design of ships (improper testing of how materials reacted to frigid ocean temperatures) to safety regulations (the lifeboat number actually exceeded what was believed to be sufficient for ships of Titanic's size) to human arrogance (challenging speed records, more of the part of the ship's owners, the White Star Line, as they wanted to sell tickets first and foremost). It is therefore dishonest to attempt to blame the sinking on one individual or group.
Given this reality, like so many things in history, we must learn from the disaster of the Titanic collectively, rather than doing a specific thing based on assigning blame to a singular factor. This is doubly so, as overcompensating for one weakness can just cause others to emerge if you don't favor a moderate and thorough approach.
Indignation may make people feel good or give closure, but it rarely helpful in addressing problems in the long run. Humanity rarely makes mistakes because we know they will happen, as they are often the result of all manner of factors that cannot be foreseen. Whether people want to or not, we can only try to do our best and learn from the past, as it can definitely be said that future disasters are inevitable due to the nature of society, increasing complexity in design, and simple lack of foresight amid myopic concerns, be they success, money, or the pursuit of records/accomplishments.
You would have to consider the captain, Edward Smith to blame for the disastrous ending. There are a number of reasons to assign fault to the captain. The decisions of the captain throughout the film were irresponsible. The captain was provided with warnings of icebergs the morning of the collision. Smith considers proceeding with caution, but hubris tends to get the best of him. This is his last journey across the ocean and he wants to make a splash (pun intended) when he arrives in New York. Members of his crew convince him there is no danger and that they should proceed full speed ahead.
A captain also displays a lack of leadership after the ship has hit the iceberg. His crew is looking for guidance and he seems to be in a daze. It is his responsibility to prepare his crew for emergencies as the captain of the ship. The entire second half of the movie demonstrates a lack of preparedness on part of the crew. It took hours for the crew to mobilize only a small percentage of passengers to the lifeboats. The entire process was inefficient, which speaks volumes of the leadership of the captain.
A case could be made that the ship's architect should be blamed for the disaster because of the insufficient amount of lifeboats on the ship. This error pales in comparison to the culpability of the captain, at least in the portrayal from the movie.