West Ham United take in a meeting with capital rivals Chelsea on Saturday.
And Bilic has confirmed that the atmosphere in the dressing room is good - although he is keen to ensure that his players do not get carried away.
"The mood here is very good," the Croatian boss said. "There is no better way to gain confidence than by winning matches and playing well.
"And there is nothing wrong about being positive under one condition: you have to know your basic jobs and respect that doing those well got us into this position. It didn’t come out of nothing. It happened because we stayed grounded and did our work.
"We then have a chance against any team in the Premier League."
Ordinarily a match against Chelsea would be quite a daunting prospect for West Ham, but Jose Mourinho's side have been in poor form this term.
The Blues have looked far short of their best, and they are still languishing in the bottom half of the table.
It leaves West Ham with a great opportunity at Upton Park, and if they are able to claim three points from the match, it would strengthen their position in the upper echelons of the division.
West Ham have already beaten Liverpool, Arsenal and Manchester City this term - albeit away from home - and a win over Chelsea could elevate them as high as second in the table.