Lukaku had been struggling with an ankle problem in the build-up to the match, and United boss Jose Mourinho revealed that it was the Belgium international who decided to start on the bench.
The 24-year-old came on in the latter stages of his team's 1-0 defeat to Chelsea, but Murphy has blasted the striker for making himself unavailable to feature from the outset.
"I've never once, in my whole career, said that I can't play when asked if I could - unless I physically can't run about," Murphy told talkSPORT.
"I've played with all sorts [of injuries]. Some players feel like they have to be 100% to play. If that were the case, I'd never play. United fans must be absolutely fuming if that's true.
"If he's got something pretty bad and thinks he's struggling, you can't go on the bench. What if Marcus Rashford had come off? The manager should've said to him 'you're starting, if you can't start then don't go on the bench'."
Lukaku, who scored 27 times for United during his first season at the club, will represent Belgium at the 2018 World Cup.