The Red Devils sold Lukaku to Inter Milan for a sizeable fee in the summer.
They also allowed winger Alexis Sanchez to leave to the Italian club on loan.
But no attacking players were signed in the summer, apart from Championship winger Daniel James from Swansea. And Bosnich believes that was a mistake.
"Let's be really frank, the recruitment has been poor over the past three or four years," Bosnich told Omnisport.
"Regardless of what the personal situation was, it was a mistake to let Lukaku go without having a ready-made replacement to come in. Especially at that stage of the season.
"They didn't [sign a replacement for Lukaku] and now Martial, Rashford and all of them have to find their spirit, find their soul and fight back.
"There's no use just sort of turning up at training, doing your job, going to the game, hiding, hoping that you don't get any criticism and picking up your wages. That doesn't work at a club like Manchester United."