Sturridge will miss Wednesday's League Cup clash against Bournemouth, with Liverpool manager Jurgen Klopp unable to put a timeline on his return.
The 26-year-old suffered a knee injury over three weeks ago, having missed the Reds' first eight games in all competitions this season with a hip injury.The England international has been plagued by injury in his time at Liverpool, making just 12 appearances and scoring four goals last term.
Fairclough, who won six league titles with the club between 1975 and 1983, believes there may be something psychological behind Sturridge's continued absences.
"Daniel has real star quality but he has to work on his attitude and desire," Fairclough told Talk Sport.
"Picking up these little knocks – surely from time to time they aren't as bad as first feared?
"Maybe the medical team offers players excuses because the modern footballer would not have gone through the pain barrier like older players did.
"You do have to be careful but sometimes you hope people show their grit and determination and put it aside to get out there."