Sakho missed West Ham’s 2-0 defeat to Watford last weekend, after picking up a problem in training, and he has not made it back in time to face Everton on Saturday.
And the Croatian manager admits that Sakho’s absence is a frustration, as he plays such a key role in his side’s starting line-up.
“Diafra Sakho is still out, it is nothing major, he did normal training on Thursday last week but then felt something in his thigh," he explained. "Unfortunately it is a small tear and he is out for Saturday’s game. He should be back for our first game after the international break.
"It’s a setback because he’s a very important player for us, he does a lot for the team and the way we are playing. He has energy, he is impulsive and he dictates the rhythm of the game."
Andy Carroll was handed a start in West Ham’s match against Watford last weekend, but the striker did not manage to take his chance.
Carroll contributed to the conceding of a goal in the Hammers’ 2-0 defeat, and his performance rather highlighted just how important Sakho is to Bilic’s team.
Sakho’s pace stretches opposition defences, and that in turn creates the space that Manuel Lanzini and Dimitri Payet need to thrive.
West Ham will be hoping to cope better without the Senegalese striker against Everton, though, as a win in that fixture could take them back into the Premier League's top four.