The Netherlands international agreed a three-year deal at Fenerbahce on Sunday after dropping down the rankings at Anfield.
"My last season at Liverpool wasn't the best one," said Kuyt. "The club was great, the people were great and the people from Liverpool - the text messages, the phone calls, the emails, all the tweets I had on my Twitter account - it's unbelievable how much respect they showed me and it's also a bit emotional.
"I thought that I should've played more so, after six years, I just had a feeling I needed to change something in my career, a new experience, a new country, new people around me, and that's why I made the decision to leave. I had a great time and I had great teammates. They wished me good luck and they said that they will miss me."
Kuyt moved to the Premier League outfit from Feyenoord in 2006.