The Iron were crowned champions in 2006/07 despite failing to win any of their opening six games in all competitions - including going out of the League Cup to lower league opponents in Lincoln City.
Murphy sees parallels to Coventry's troubles adapting to life in the third tier, which has already cost manager Andy Thorn his job.
The Sky Blues dropped to second-bottom in the table on Saturday after losing 2-0 to Tranmere, their third straight defeat.
"We need to sort this out very quickly and it isn't [caretaker manager] Richard Shaw's fault, it's ours really. The two goals we conceded were not good enough and we have to take our chances. It isn't up to a manager to defend and score goals for us," said Murphy.
"But I am sure we will do that. I was in a similar situation at Scunthorpe. After six games, we hadn't won a game but we sorted the problems out and went on to win the league.
"The lads were talking about how you can get used to losing. We played quite well on Saturday and looked like the team who were going to win it. But when one thing goes wrong, things just snowball."