The Hammers are currently only six points away from the Champions League places, but Bilic wants to lower expectations.
The Croatian boss insists that he side still have a long way to go if they are to make it into Europe’s premier competition.
He said: “We don’t have that kind of ambition. We’re very far away from Champions League. All that we want it to continue to play like we are playing, pick up the points and see where that takes us. But we should be happy and all West Ham fans should be happy that we’re playing like we’re playing.”
Despite Bilic’s attempts to cool expectations around Upton Park, if his side keep delivering impressive results talk of them claiming a European spot will only grow louder.
The Hammers’ next two matches are against struggling Aston Villa and Sunderland, and Bilic admits his side could become victims of their own success.
"You’re right [that supporters will want more if West Ham’s good form conitnues],” he added. “But it’s good. You are becoming a victim of your own success. But that’s the same for everyone and you’d want to be in that position rather than the position of Aston Villa.
West Ham are set to host Aston Villa tonight and they will be heavy favourites to win the match.
Villa have had an awful season to date, and currently sit 10 points adrift of safety after winning just two of their first 23 league matches this term, and it would be quite a shock if they got one over the Hammers this evening.