West Ham have fallen to just five points off the relegation zone after winless run of seven Premier League matches.
Tonight's 3-0 defeat to Arsenal means they've now lost five games on the bounce and will only fuel reports suggesting the club are looking to replace Bilic in the summer.
The Hammers manager admits his side are in danger of going down this season but has told his players to focus on Saturday's visit of fellow relegation candidates Swansea (3pm).
When asked if West Ham are in a relegation battle, Bilic told BBC Sport: "Of course we are. We don't have to hide it. It's not being negative, it's being realistic.
"I told the players to forget today – we have big games ahead of us. It's a massive game against Swansea on Saturday.
"We are in a fight to keep our Premier League status. We have to start winning games.
"To get that confidence back is the key point. One win will change everything for us. Because three points at this stage of the season are massive."
After a dull first half at the Emirates, Mesut Ozil, Theo Walcott and substitute Olivier Giroud all scored at the Emirates to pile the pressure on Bilic.
And the Croatian boss concedes the Gunners were the better side on the night.
Bilic added: "Arsenal deserved to win. The first half was OK, not only because of the score but we were good.
"We defended well with numbers. And we were also good on counter-attacks.
"In the second half they raised the tempo and scored a goal, and they were the better team. They were sharper than us tonight.
"We wanted to keep a clean sheet and the draw as long as possible, or even better to score, and make their fans and players a bit more nervous.
"But they started to play with more freedom after scoring."
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