At the climax of the film Irina asks the aliens to give her knowledge of all things, and is subsequently destroyed. There are 3 possible reasons this occurred: (1) The aliens, being psychic, sensed Irina's evil intentions and destroyed her for them. This theory is supported by the malevolent look on the alien's face as she disintegrates, (2) The aliens do exactly as she asks, but her primitive human brain is ill-equipped to handle the sudden surge of cosmic knowledge, causing her brain and (as a result) her body to spontaneously combust. This theory is supported by her yelling out "It's too much!" during the info-absorbing process, and 3) It was actually both. The alien was willing to grant whoever returned the 13th skull 'a gift.' Sensing that Irina's intentions were both for greed and evil, he gave her exactly what she wanted, knowledge of all things, even though it killed her, which is why of course all our heroes make it out alive. They were respectful of the aliens' powers and chose to leave with their lives instead of being granted any form of powers.
The most conventional reason, however, may be associated with Irina's line that the aliens are " One being, physicaly separate but with a collective consciousness; more powerful together than they could ever be apart." Knowing this, add the alleged fact that Irina has some sort of "psychic" ability with the notion that the collective being seen at the end can read her thoughts, and it's apparent that it would realize that Irina had no intentions of using their "gift" for any good purpose, thus destroying her for the greater good. (Of course, as an aside, it's worth noting that while Irina claims to be a mind reader, she never actually demonstrates any such power; her one attempt to do so fails. It's entirely possible that she, like the average claimant of psychic powers, was faking the ability to gain greater status.) Also, given that Indy tells us that the inter-dimensional beings' treasure is knowledge, it would indicate that the skull, being intelligent and possessing wisdom, refused to communicate with Irina (remember she had to use both Ox and Indy to communicate with the skull and the combined being speaks Mayan through Ox at the end of the movie), knowing through its psychic ability, that she has always had ill intentions. This adds up to her never being the intended recipient of the gift from the inter-dimensional beings to begin with.