The Croatian has guided the Hammers to third in the Premier League since taking over in the summer and increased the pressure on Chelsea boss Jose Mourinho by overseeing a 2-1 victory over the Blues last weekend.
The win adds to the other scalps of Arsenal, Liverpool and Manchester City with Bilic enjoying a fine start to his managerial career in England.
West Ham travel to Watford on Saturday looking to maintain pace with the front-runners but Bilic insists there is plenty of room for improvement from his squad.
"It has been a good start and we are enjoying it but we are on the ground totally," he said.
"It is only a start but we are confident, we are playing well and if we continue to work hard as we have since day one, of course there will be ups and downs results-wise, but I don't see a reason why we should drop dramatically.
"The core of the team has been playing together for some time now and that is the greatest thing, we only added some players we thought were necessary to make the team better.
"It is still early days to say where the limits are for this team - what is definite is that we have lots of room to improve from every aspect."
When asked to specify what areas he was specifically talking about, Bilic replied: "Everything.
"Some players know each other only for a couple of months so we can improve organisation and transition.
"We can improve small things like set-pieces and second balls
We definitely have to improve in shooting because we are not shooting enough
That doesn't mean I'm not happy with the performances so far but we can improve in absolutely everything."
Club-record signing Andy Carroll came off the bench to head the winner against Chelsea as the England striker returns to full fitness.
With Enner Valencia also closing in on a return, Bilic admits he will soon have a selection dilemma on his hands - while backing the England contingent such as Carroll, Mark Noble, Aaron Cresswell and Carl Jenkinson to push for a place in Roy Hodgson's squad.
"Now I have a positive headache, I have many good players who deserve to be selected in the first 11 or the 18 but I have to make the choice," he added.
"We have most of the players back and I'm glad of it, our medical team has done really well
We are planning that if someone is tired he will get individual training and stay in the gym to protect them from injuries.
"I was the manager of my country (Croatia) for six years
I don't want to tell the England manager who he should pick or not, especially after winning 10 games.
"They have the best record in Europe but of course we have some good players and I rate my players.
"If they continue to play like this they have every reason to hope they are going to be involved in the England team."
Source : PA
Source: PA