The phrase "acknowledged to himself" is grammatically correct and can be used in written English.
It is often used to describe when someone privately accepts or admits something to themselves. Example: After years of denying his true feelings, John finally acknowledged to himself that he was in love with his best friend.
As the story ends, he and the housekeeper are enjoying their time together, but he has acknowledged to himself that it will be brief.
He had been attending AA meetings for three years at the insistence of his family but had never acknowledged to himself that he had a problem.
Joshua, who was a freshman at Curry College, about 40 miles north of Brown, had also recently acknowledged to himself that he was gay.
Matt writes that he never fully acknowledged to himself that he was gay until his sophomore year in college.
Danilo, who was beginning to acknowledge to himself his feelings for Hanna, is furious, and he leaves to drown his sorrows at Maxim's.
Antony's behaviour is often appalling (something he occasionally acknowledges to himself), but it is his appetite for adventure and excitement that is a magnet for Lily.
Rather, it is about Salieri's fury with God when he is forced to acknowledge to himself that his own talents as a composer come to nothing when compared to those of Mozart.
I think he is an earnestly liberal, politically correct guy who genuinely believes in the stated aims of feminism, at least as far as equality goes, but I think he also harbors a good deal of reflexive sexism, some of which he is unaware of and some of which he acknowledges to himself but instinctively refrains from revealing to others.
It's not something he's ever talked about before, that he didn't even acknowledge to himself until a few years ago, when he was in therapy at the Hoffman Institute, but between the ages of 10 and 12 he was sexually abused by an older girl.
In 1985 Mr. Cooper moved to Amsterdam in pursuit of love and, he acknowledged, to rid himself of a drug habit.
After Pacquiao dominated and destroyed De La Hoya, who then retired from the ring, the Golden Boy acknowledged to Roach himself what the veteran trainer had been saying all along.
