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."

Up to 170,000 football fans are expected to travel to the capital to watch the showdown between Juventus and Real Madrid on 3 June.
It will be the first Champions League final to be played under a closed roof.
The Football Association of Wales (FAW) said safety was a "primary objective".
The roof closure had been suggested because of fears of a drone attack on what is described as the biggest club football game in the world.
After discussions with stakeholders, the FAW, said it had made the decision to close the roof after taking into consideration "recommendations made by the authorities".
The roof will also be closed for the two official training sessions to be held at the stadium on Friday 2 June.
Juventus and Real Madrid have been informed of the decision.
In a statement, the FAW said: "The 2017 UEFA Champions League final will be the first final to have been played under a closed roof and will further amplify the stadium's atmosphere when Juventus FC take on Real Madrid CF on Saturday 3 June."
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.
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The roof of the National Stadium of Wales will be closed for the 2017 Champions League final in Cardiff for safety reasons.