Carroll completed 90 minutes in a Premier League game this term for just the fifth time vs Arsenal
The former Newcastle and Liverpool striker produced one of the finest individual displays this season as his hat-trick all but ended Arsenal's title challenge.
It also pushed Carroll into contention for an England Euro 2016 spot but Bilic knows the Geordie must find a solution to his own fitness problems.
"I'm not blaming him but it's a fact that he's out every now and then," he said. "And it's a fact that when he's got consistency he's like he was in this game.
"As a medical team, as a club we're doing everything, so he's got to do something. He's doing it but he should be even more dedicated to stay away from those injuries for a few years. Because it's a waste for West Ham and probably for England. It's a waste for big clubs if they want to buy him from abroad.
"He goes to bed at 10, he should now be going at 9.30. But he has to do something. I'm not a medical expert or voodoo, I'm just his manager who's just thinking about that and I know he loves football. It's not the training because when he trains, he loves football.
"Ideally you don't want an opponent an easy header."
Wenger played David Ospina in goal despite Petr Cech's return to the squad following injury. But the Frenchman insists the former Chelsea man will regain his spot once he is fully match fit.
West Ham (4-3-3):Adrian 7; Tomkins 5 (Emenike 46, 7), Reid 7, Ogbonna 6, Cresswell 7; Kouyate 6, Noble 6, Lanzini 7; Antonio 7, Carroll 10, Payet 8. Booked: Carroll, Antonio. Goals: Carroll 44, 45, 52. NEXT UP: Manchester United (h), Weds FA Cup.
Arsenal (4-2-3-1):Ospina 7; Bellerin 6, Gabriel 6, Koscielny 7, Monreal 6; Elneny 6 (Giroud 68, 6), Coquelin 6 (Ramsey 61, 7); Iwobi 8, Ozil 7, Sanchez 7; Welbeck 6 (Walcott 82). Goals: Ozil 18, Sanchez 35, Koscielny 70. NEXT UP: Crystal Palace (h), Sun PL.
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