The West Ham striker sustained his latest injury - to his thigh - at Sunderland last weekend but managed to complete the game, which ended in a 2-2 draw.
Fortunately for the Hammers, Carroll's wayward effort fell at the feet of Andre Ayew, who tapped in the opening goal at the Stadium of LIght.
And according to Italian sports daily Corriere dello Sport, the Hammers are set to make a shock move for Lazio boss Inzaghi as a potential replacement for Bilic in the summer. "He felt it in the beginning of the game".
He felt it in the beginning of the game, we can talk about a miskick or an assist for Andre's goal but he said at that moment he felt it.
"He had a scan after the game and although it showed nothing major, it is serious enough to rule him out of this game". Bilic added: "Winston is one of the most important players for us".
Ronald Koeman's side are seen as favourites by many going into the contest and Bilic admits his players will be facing a much higher quality opponent than they have in recent weeks.
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He scored the first goal for Los Blancos with a very good play, dribbling two opponents and scoring from a great let footed shot. Barcelona stayed firm behind Real Madrid in the title race by winning 3-2 against Real Sociedad at Camp Nou.
The relationship between Bilic and Sakho has reportedly hard between the pair, with the striker close to leaving the club last summer, but for the move to West Bromwich Albion falling short to a failed medical.
"It was in the 'papers that I had a row with Diaf, but no, there is no rift between us", he told the club's official website.
Luckily they face a West Ham United side that is once again in crisis.
Terry was with the Hammers until he was 14 before switching from hometown Barking in East London to Chelsea. I'm a big admirer of John, he is one of the best that ever played.
"He's won everything, done everything, we are talking about the England captain, a good leader and all that but we are pretty well covered in that position".