Again, you don't say what your nationality is but with this link, you can change it. I used Austrian for you as you say you departed from Innsbruck.
These are the entry requirements into Costa Rica and as you can plainly see, you are required to have onward tickets. If you're saying that because it doesn't say the tickets have to be within the validity of the visa that it's ok to not have it, it also doesn't say you can't kill someone when you're there but you still can't do that.
http://www.timaticweb.com/cgi-bin/ti...&subuser=PEARL
It is inferred that you have valid tickets and documents for your next destination within the validity of your visa length.