Cagliari owner Cellino, still waiting for the Football League's approval of his B£25million bid to take control at Elland Road, attempted to sack McDermott after reaching an agreement with current owners Gulf Finance House Capital.
But contracts on the purchase of 75 per cent of the club's shares had not been exchanged at the time and GFH overruled Cellino, insisting McDermott would not be forced out while they retained ownership.
Cellino has since said he is willing to work alongside McDermott and has provided the former Reading manager with the funds to bring in Stoke goalkeeper Jack Butland and Sunderland striker Connor Wickham on loan in a bid to rekindle Leeds' play-off hopes.
"The way he has dealt with it all has been first class," said Murphy after helping to promote the Leeds United Foundation's 'Tackling Track Safety' with Network Rail and primary school children at the city's railway station.
"He's never let his standards slip or anything like that. He's kept his head held high and got on with the job as usual.
"It's a situation nobody deserves to be put through, especially someone who deserves the respect for what he's done throughout his career."
Murphy, 24, was signed by McDermott from Crewe in the summer for a fee understood to be in excess of £1million.
"He obviously brought me in and I've got huge respect for him and I'll always owe him a lot for that and giving me my chance in the Championship," Murphy added.
"I was sad to hear he got the sack and when he got reinstated it was great news for everyone at the club - as everybody showed with their support towards him."