There used to be a time when English virgins who were about to embark on their first sexual journey–on the eve of their wedding night–were given this piece of homely advice
close one's eyes and think of England
also known as
lie back and think of England
It's definitely outdated and I'm not sure if anyone nowadays offers this advice to anyone who is sexually inexperienced or dislikes making love. But the sentiment behind it is similar to the one described by the OP. Bite your lower lip, don't think about what is happening (shudder), just endure it until the act is over. Unfortunately, it's not the single word requested by the OP but most native people would understand its meaning,
Supposedly advice given to women whose husbands were soon to attempt to have sexual intercourse with them, encouraging them to think of how beneficial children (who could grow up to be soldiers, sailors, merchants, etc.) were to England.
TV Tropes elucidates
It's possible the phrase was invented as a joke on the assumption that Victorian and Edwardian ladies were prudish in the extreme. Keep in mind, though, that in this time period it wasn't unheard of for a woman of a high class to have to choose between marrying a strange man many years her senior who had no interest in pleasing her, and suffering serious societal repercussions including being possibly left penniless when her parents died. In other words, lying back and thinking of England may have been the best of bad options.
It has been attributed to Queen Victoria but the author of The Phrase Finder soundly rebukes this theory
'Lie back and think of England', or as it is more often expressed these days 'close your eyes and think of England', was used in two contexts. Firstly, it was, or later dramas have portrayed that it was, advice given by a mother to her daughter on her wedding night. Sex education wasn't all that it might have been in the early 20th century.
The other context is of advice given by a woman friend to a loveless wife. Marriage was a route to economic security for women in Edwardian England and many must have seen the granting of sexual favours as an unwelcome price to pay for it.
The expression is sometimes attributed to Queen Victoria […]
There's no evidence that Queen Victoria ever uttered the phrase and circumstantial evidence points entirely the other way as she loved her husband deeply, was an enthusiastic sexual partner and the couple had nine children.
In the OP's sample sentence, it wouldn't sound out of place
"I often thought about what I felt. If I were to use an expression to describe it, it would be close one's eyes and think of England, but essentially I made love to him not because I enjoyed it, quite the contrary, I did it because I cared about him and wanted him to have a good time even though I didn't like it."