The Hammers have picked up just one win at Upton Park this season but made it four on the road on Saturday when they added Crystal Palace to the scalps of Arsenal, Liverpool and Manchester City.
They host Chelsea next weekend with boss Bilic urging his side to show the same patience they do away from home, rather than play as if they have a time limit in which to shoot.
"We don't say 'away we are going to play like this, and at home we are going to play like this'," he said
"But sometimes you have to change.
"We will try to win our home games and maintain our away form, but it's more that we started sloppily in a couple of home games.
"At home sometimes we are playing like it's basketball and you have a limit of 24 seconds to finish your move, and you are forcing the situation too early.
"Away we are a little bit more patient, but at home not patient enough."
West Ham certainly had to show some patience at Selhurst Park, with Palace holding out until the 88th minute with 10 men.
Carl Jenkinson's opener had been quickly cancelled out by Yohan Cabaye's twice-taken penalty but the game turned on Dwight Gayle's dismissal, for two reckless challenges, on the stroke of half-time.
The Hammers finally broke Palace's resistance when Manuel Lanzini lashed in Andy Carroll's knock-down with two minutes remaining, and Dimitri Payet added the gloss in stoppage time.
Bilic's side are now up to the heady heights of fourth but the Croatian is still playing down what they can achieve this season.
"At the club we have no expectations," he added
"You can't stop the fans' (expectations) - unless you start losing, and that is not what we want.
"But our target is to stay in the league
It's early days, not late May
Our target is to play good football, to be solid, defend and attack with numbers and keep the ball, score more goals and get more points
Where we will finish, I don't know! But it should be good."
Defeat was harsh on Palace but manager Alan Pardew tried to look on the bright side.
"The resilience we showed in the second half, down to 10 men, was a good sign," he said
"At some point it will happen to us - a team will go down to 10 men and we will have to exploit it like West Ham did to us."
Source : PA
Source: PA