That's how Anakin saw Palpatine; somebody he could trust and confide in, a mentor figure who really understood him because he wasn't beholden to all those inflexible and frustrating rules of the Jedi Order, and recognized and encouraged Anakin's potential in ways that the Jedi weren't doing. In reality it was just Palpatine manipulating him and getting Anakin more and more under his control.Well, Palpatine was Anakin's closest friend and ally.
I vaguely remember in one of the comics there was a Jedi who was human but grew up with a Tusken tribe or something, and Anakin told him about killing the Tuskens. But he didn't spill the beans to the Council.
Also, from the movies and Clone Wars, it seemed that Anakin never told Palpatine about his marriage, or his fear of losing Padme. That was the one thing he didn't dare tell anybody. He had vaguely asked Yoda about premonitions of losing someone, but didn't go into detail about who (whom?). So in ROTS when Palpatine gave him that line about "you will be able to save your wife from certain death," it was clear that Palpatine was more than met the eye, along with the revelation moments before that Palpatine knew the ways of the Force.
Kor