Much has been said of West Ham's unbeaten away run, after their high-profile victories over Arsenal, Liverpool and Manchester City, however, they proved their mettle at home on Saturday when they beat champions Chelsea 2-1.
With the Hammers currently on a seven game unbeaten run in the league, Bilic said it was too early to determine whether his side will find themselves fighting for European spots in May.
"We are only a quarter of the way through the season. To be honest, I don't even think about football like that. One quarter, so what? All we want to do is concentrate on the next game," Bilic told the club's website (www.whufc.com).
"If we drop (our level of performance), by even five percent then we are in trouble. We have to be in what I call the red zone all the time, we can never be in the comfort zone, and it can take ages to get out of it. So we can never be carried away.
"Only when it is five games to the end of the season or so that we can concentrate on the league positions."
Defender James Collins reckons the Hammers can finish high up the table if they can sustain their current form at least until Christmas.
"We have got the squad to do it. That's the major thing. We've got competition for places in every position," Collins said.
"The squad this year has been improved so much that if we're there, or there abouts, around Christmas, there's no reason why we can't sustain that and finish there."
Collins has also heaped praise on striker Andy Carroll, who scored the winner in Saturday's game against Chelsea.
"Any team in the Premier League would be delighted to have Andy Carroll on the bench," the 32-year-old said.
"If I was on the defending team and Andy Carroll was coming on, I wouldn't be too happy about it. If you play the right ball to him I think he's unplayable at what he does."
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Sudipto Ganguly)
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