Christiansen has waited to make a public response to the club's decision, but has chosen to credit the club's fans in a post on social media.
On Instagram, the 44-year-old said: "I did not want to leave without saying goodbye to you, the fans.
"You are the most precious treasure of this wonderful football club. Managers, players, directors and presidents may change, but you are the ones who remain, together and united.
"Your passion and requirement for success just symbolises your strength. Thank you for all your support."
Christiansen recorded 15 wins and six draws from his 35 games in charge.