The former Swansea defender, who played for the Welsh team during their rise to the top flight and took over from Michael Laudrup as boss in February 2014, issued a statement through the League Managers' Association on Thursday.
"I believe that whenever you join a football club, the supporters deserve your blood, sweat and tears. I can say for sure I gave all those things and more," he said.
Monk earned plaudits for Swansea's 2014-15 campaign when he steered the club to a record eighth-place finish.
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They started the current season well, drawing with Chelsea on the opening day and beating Manchester United at the end of August.
Since that victory, however, Swansea have won only one of 11 matches and have plunged towards the relegation zone.
"Everyone at the club from myself, my staff and the players themselves have been working tirelessly to change this loss of form, but unfortunately have not been able to in satisfactory time," Monk added.
"I have no doubt whatsoever that these players will start to show their true quality again very soon, and the club will be looking upwards once more."
Monk joined Swansea when they were in the fourth tier and was a cornerstone of their defence as they earned three promotions and returned to the top flight in 2011 after an absence of 28 years.
He captained the club in all four divisions and made 270 appearances before taking over as manager on an interim basis when Laudrup departed.
He was handed the job on a permanent basis in May 2014.
"I would have liked to continue because I strongly believe we would have come through this period together and stronger but I will now use my time to reflect and improve, ready for my next challenge," he said.
(Reporting by Toby Davis; editing by Ed Osmond)
