Peacock joined Rovers at the start of the season, but was unable to help them avoid relegation to the Championship.
The 38-year-old came out of retirement in September, playing his fourth game of the season in Saturday's defeat.
"I always want to be accountable for my actions in life and offered my resignation after the game," he said.
"This was turned down which means I can continue my journey with this great club.
"While relegation hurts, it allows the club to stop just trying to change the branches and begin a full root-and-branch overhaul of the rugby department, building rock solid foundations that will enable this club to rise again."
Hull KR players had criticised the Million Pound Game format in the build-up, with their Super League contracts automatically becoming void as a result of their defeat.
"To be in a dressing room with grown men, wives and children crying is not what sport is about," Peacock added.
"To be part of a club with such loyal, passionate support is very humbling and the reaction after such a defeat will stay with me for life."
Hull KR have rejected head of rugby Jamie Peacock's offer to resign following the club's defeat by Salford in the Million Pound Game.