There are two opinions that histories have, when dealing with this question. Some historians say that the appeasement wasn't justified and that Chamberlain was a weak person while of the other hand some say that Chamberlain didn't have any other chose. There are a number of reasons that support both of the sides.
Appeasement was justified in a few ways, sympathy for Germany, the desire for peace, the threat of communism and the time to rearm. All of these factors explain how the appeasement was justified.
Sympathy for Germany, was an accept that mainly concerned the British. As a matter of fact the British thought that the treaty of Treaty of Versailles was too harsh on Germany. In addition Briton had an opinion that Germany should be treated more fairly. And as a consequence the British gave away on many things that Hitler desired, even when going against treaty of Versailles.
For example the British signed the Anglo-German Naval Agreement in 1935. Which allowed Germany to have a navy. Further more The British didn't take any actions when Hitler invaded Rhineland. Subsequently, nothing was done to stop Germany from joining with Austria. The British hoped that Hitler would get satisfied and stop his demands.
The desire for peace is the second important factory which makes the appeasement justified. Remembering the First World War, Britain and France didn't want something like this to repeat again. They wanted to keep the world in peace. People from these countries didn't want another war and hoped that the League of Nations would have the power to settle quarrels between countries. Furthermore there was the Great Depression that put many countries into a position, where they simply couldn't afford a war.
The Threat of communism, also explains why the appeasement was justified.