Daedrova said:
Was my action wrong? Were they justified to leave me to face such a danger alone?
Hm. Seems to me that neither side actually has the information necessary to have an informed opinion on the morality of killing the beast.
The tarrasque is not an "innocent". By the book, it pops up every year or two, and rampages across the countryside. This is not a sleeping doberman who might bite someone. This is a sleeping doberman who is well known as a vicous brute who attacks and does great damage. The darned thing eats whole villages, for crying out loud!
However, that doesn't mean it is a good idea to kill it. If, for example, the tarrasque makes younger dragons a major part of it's diet, removing it may not be doing anyone any favors.
But as far as you've described, your party doesn't know the consequences of removing it. So it is anyone's guess.
I don't know your players. Maybe they were accidentally applying modern morals on a fictional situation. Maybe they just were making excuses because they were scared of characters being eaten. It is clear, however, that the DM had not made clear what the tarrasque was known to be. So, while I'm not sure anyone (including yourself) was particularly well-justified, I'm not about to go knocking anyone for their decisions.