At the High Court in Edinburgh, he was sentenced to life in prison.
Fiona Holligan, procurator fiscal at Greenock, said: "This was a tragic murder of a vulnerable pensioner.
"Martin Olej had gone to Mr McCulloch's flat for a drink but ended up attacking him, pouring lighter fluid on to his carpet and setting it alight before fleeing the scene and leaving the victim to his fate.
"I am glad that the perpetrator has been brought to justice for this."
