Byram has yet to convince Bilic since his move from Leeds in January last year, and that substitute appearance against Bournemouth last Saturday summed up his impact in east London so far.
The 23-year-old overlapped superbly to set up Andre Ayew for West Ham's equaliser, only to get caught upfield when Bournemouth broke away to score a last-minute winner.
"We spoke about that and I told him that mentality is good, to be positive, to be optimistic," said Bilic.
"But there are situations towards the end of a game when some of your moves depend on the result.
"I don't want to take that mentality away from him but then again - and the whole game is about taking a gamble - but in some situations you don't take that gamble."