The club's all-time top goalscorer was dismissed on Monday morning, just a day after leading the Blues to a 3-1 FA Cup win over Luton.
Lampard wrote: "It has been a huge privilege and an honour to manage Chelsea, a club that has been a big part of my life for so long.
"Firstly, I would like to thank the fans for the incredible support that I have received over the last 18 months I hope they know what that means to me.
"When I took on this role I understood the challenges that lay ahead in a difficult lime for the football club.
"I am proud of the achievements that we made, and I am proud of the academy players that have made their step into the first team and performed so well. They are the future of the club.
"I am disappointed not to have had the time this season to take the club forward and bring them to the next level.
"I want to thank Mr Abramovich, the board, the players, my coaching team and everyone at the club for their hard work and dedication, especially in these unprecedented and challenging times.
"I wish the team and the club every success for the future."