Darryl Peacock passed away, at the age of 59, on Friday, just 24 hours after his son played a key role in the Rhinos' 20-6 win at Wigan in the final match of the regular Super League season.
Peacock, who drove himself to Wigan after leaving his father's bedside and returned to the hospice straight after the match, had dedicated his rugby to his father since November 2011 when he was diagnosed with lung cancer and given only months to live.
McDermott, who played with Jamie Peacock at Bradford, said: "On behalf of everyone connected to the Rhinos, we would like to send our deepest sympathies and condolences to Jamie, his mum and his entire family at this difficult time.
"It is a mark of the man and his dedication and commitment to our club that he played on Thursday night.
"Not only did he play, just as his dad would have wanted him to, but he was once again one of our leading players in the victory.
"We know that this has been a tough few months for the whole Peacock family but they know that they have the love and support of everyone connected to the club.
"Jamie has asked me to pass on his thanks, particularly to the media, for respecting his family's privacy following Thursday's game."
Peacock, whose outstanding form in 2013 is expected to be recognised with his selection for the Super League Dream Team when it is unveiled on Monday and a shortlisting for the Man of Steel award he won in 2003, believes his father's illness has spurred him on to produce some of his best rugby in the twilight of his career.
In an interview with the Yorkshire Post in May, he said of his father's diagnosis: "It was hard at first but it pulls you together as a family and it has made me want to play better because I think there won't be many more times he'll get to see me play.
"So last season was a big focus for me. The team knew about my dad as well and they really rallied around.
"I thought it might have been the last season (he'd see me play) and I really wanted to win the final for him.
"I think his illness is one of the reasons I'm playing so well, without a doubt. I just want him to remember me in the best possible way."
Peacock, 35, who retired from the international game 15 months ago after winning 34 caps, was awarded an MBE in the 2012 New Year Honours for services to rugby league.