The Ghana midfielder has gone straight into Jose Mourinho's side since his arrival at the club and he is convinced that it is only a matter of time before they return to their sparkling best.
"We are talking about Real Madrid, the greatest club in the world. Every player would want to be here. I'm just Michael Essien and eventually I hope everyone will know me here," he said.
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"Every game is important, and we need to earn the right to get more points and fight for the title."
Having plied his trade in the Premier League for the last seven years, his move to Spain has brought with it a host of new challenges and Essien believes La Liga provides more entertainment than England's top flight.
"People talk about the Premier League as the best, but La Liga is more fun, you play more football and score more goals," he continued.
"The Spanish league is one of the most important and difficult competitions in Europe and because of that I'm looking forward to having a good season and defending our title."
Despite moving to Spain for the season, the 29-year-old still has an eye on the results of his parent club and believes that Roberto Di Matteo will lead the Blues to their first title since 2010.
"They have a good chance, but you never know what can happen. I would still bet on Chelsea," he added.