The Hammers became just the fourth team in Premier League history to win away at Arsenal, Liverpool and Manchester City in the same season after a hard-fought 2-1 win at the Etihad Stadium last Saturday.
Those three results are more significant as they came in Bilic's first three away league games as boss at Upton Park - with West Ham sitting third in the league, just three points adrift of City.
They welcome Norwich to east London on Saturday and, with such momentous results already sealed, Bilic is keen to keep a lid on any heightened expectations after a similar start last season under previous boss Sam Allardyce petered out.
"It's too early to talk about the start," he said.
"At the end they lost a bit of motivation last season, it happened in February
But I'm not thinking about that period, all I'm thinking about now is the Norwich game
We are trying to mix the team.
"I'm just thinking about Norwich and Sunderland then we have the international break
It will be nice to win all games in the Premier League, that's our aim of course
That is important for every team we play."
West Ham lost in extra-time to Leicester in the Capital One Cup third round on Tuesday night, with Andy Carroll playing over an hour in his first start since January and Bilic has been impressed wit the England striker's application to overcome another serious injury.
"Andy couldn't do more in training," he said of West Ham's record signing.
"After seven months out, these things take time
We have to be patient and we don't want to rush him
Having said that, he can only regain that edge by playing games, so we have to find the right balance."
Like West Ham, Norwich have a strong away record and have lost just once on the road in the league since Alex Neil's appointment at the turn of the year.
They travel to Upton Park having drawn at Liverpool on Sunday and Bilic is expecting a tough test against the newly-promoted Canaries.
"Norwich are a really good team," he added.
"We know it will be a difficult game, they have started very well
We have watched a few games, they are full of confidence
They defend as a unit and are very solid.
"They are not a spectacular team but they have everything - pace, ability, size
Their last game at Anfield maybe Liverpool had just one or two chances
You can't beat them by being predictable.
"It gives us an advantage as Norwich had one day less playing Sunday, Wednesday (against West Brom in the Capital One Cup) as opposed to Saturday, Tuesday
It should give us a small advantage."
Source : PA
Source: PA