The 22-year-old joined the Dutch club over the summer and will remain there until the end of the season.
"In August I requested a transfer to FC Twente," he told Voetbal International.
"City had nine defenders in their squad. Only four of them can play and only two can sit on the bench. Even in the stands there were bigger names than me.
"I wanted to fight for my place as I am not someone to run away from a challenge. However, sometimes you have to stop dreaming, be realistic and leave."
Boyata signed his first professional contract with City in 2008 following a spell in the club's youth system.