The Spaniard joined the Blues for a British transfer record of £50m in January 2011, with the majority of Reds fans still holding a grudge about how he was perceived to have downed tools in an attempt to force through a move late in the January window.
Speaking to AS to coincide with his 30th birthday this week, the Spain international said: "They haven't understood because all they've been told is the version that some people have given the club and the media.
"They have been sold something which isn't reality. I'm sure it's not easy to understand when a player leaves, but I have the thousands of letters I've received in London from Liverpool fans thanking me and now following me in another team.
"Last year we went to play at Anfield and a man over 70, almost in tears, thanked me and wished me the best. There will be every kind of reaction, but the Liverpool fans I have come across have had loving words for me."
Chelsea are currently top of the Premier League.