I've not come across any such source about what Hooker thought about the outcome of Gettysburg. However, my educated guess would be that Hooker would have quietly claimed some degree of credit for the Union victory in the knowledge that he had commenced the movements of the AotP in the overall campaign that eventually led to the successful outcome. Moreover, Hooker was not relieved because of any particular egregious error he made during the lead-up to Gettysburg. Rather as
@rpkennedy has noted, Hooker's legitimate request for the Harpers Ferry garrison was simply the Lincoln administration's pretext to move Hooker out of army command. But Hooker was a sly enough schemer to also realize that his best bet was to swallow his wounded feelings and root for the home team in the hopes that he would not be shelved, but be given a serious role. And that is in fact what happened: Hooker subsequently commanded the XX Corps in Tennessee, for which he had a respectable tenure.