Former West Mercia police officer Benjamin Monk, who was dismissed at a fast-track disciplinary hearing after being found guilty of manslaughter, was jailed for eight years following a trial at Birmingham Crown Court.
During the trial jurors heard that the Telford-based officer had used excessive force in dealing with the retired footballer.
Bishop Dr Desmond Jaddoo, of the Justice 4 All Coalition, has since started an online petition at change.org calling on the Ministry of Justice to extend Monk's prison sentence.
It has been signed by more than 1,200 people so far.
The petition states: "The judge in his ruling gave what he described as a minimum sentence despite this officer placing the Atkinson family, friends and the community through the full ordeal of a trial following the incident in August 2016, for which it is asserted that he showed no remorse having been found guilty of manslaughter with his unlawful use of force.
"We request your support in demanding that this sentence be increased to 15 years, that would ensure accountability that the life of Dalian Atkinson mattered. "Although this is the first conviction of a police officer and sentence in direct connection with the death of a black man, the sentence of eight years with a possible release after five years is far too lenient.
"Therefore, for the sake of equality and natural justice we call for this sentence to be reviewed by the Ministry of Justice and that it be increased to a minimum term of 15 years."
The petition can be found at change.org/p/ministry-of-justice-increase-the-sentence-of-pc-monk-for-the-manslaughter-of-dalian-atkinson.
Monk was cleared of the ex-Aston Villa player’s murder but convicted of his manslaughter following a trial which heard he Tasered him with an excessive 33-second deployment of the weapon, and then kicked him at least twice in the head as he lay collapsed on the ground.
Mr Atkinson, 48, was pronounced dead in hospital shortly after the incident outside his childhood home, in Meadow Close, Trench, on August 15, 2016.