Adams and coach Ian Salisbury were shown the exit door on Monday following a poor start to the season. Adams released a statement admitting he had hoped to continue his rebuilding programme at the club, which was rocked by the death of batsman Tom Maynard last season.
"Clearly I am disappointed not to be able to continue the building process," Adams said. "I felt with the squad I put together and particularly after the devastation of losing Tom Maynard last year, this would be a strong year. There is still so much to achieve in 2013, particularly in the T20 competition where I expect the team to go all the way."
He added: "I now look forward to furthering my career in coaching and management and would like to wish Surrey CCC every success for the remainder of the season and beyond."
Surrey are yet to win an LV= County Championship First Division match despite an ambitious winter recruiting campaign that netted South Africa skipper Graeme Smith and Australia's all-time leading run scorer Ricky Ponting.
Their arrivals prompted predictions Surrey could challenge for the title - just two years after Adams steered them back into the top-flight.
But little has gone right since, with skipper Smith suffering an long-term ankle injury, and with performances falling below expectations the club reacted by bringing in former England captain Alec Stewart to take temporary charge.
Adams was recruited in a high-profile move from Sussex in 2008 but the primary success during his time at The Oval was 2011's Clydesdale Bank 40 Trophy and the club's heavy investment demanded more, but despite the winter activity a return to the Second Division remains a possibility and they face a trip to leaders Yorkshire on Friday.
Adams defended his record, saying: "I have thoroughly enjoyed my four and a half years with Surrey and am enormously proud of all we have achieved together as a team, especially winning promotion to Division One and winning the CB40 Final at Lord's.
"The last 24 months alone has yielded more England representation across all age groups and development squads, all the way up to full international honours, than at any other time in the club's history."