The Hammers right-back insists the players now fear no one in the division.
The Hammers currently sit fourth place in the Premier League - just two points off the top - having won six and drawn two of their first ten games.
The manner in which Slaven Bilic has got his team playing and their scalps against some of the biggest teams in the division has sent expectations through the roof at Upton Park.
Fans have started to believe this could be a special season and Cresswell insists confidence is equally high among the players.
"We are going into each game full of confidence," said the 25-year old, in quotes published by the London Evening Standard.
"We don't fear anyone, whether we're away or at home against the top sides.
"We try to win every game and must continue the form we are in, especially on the road."
The Hammers have already secured famous away wins against Arsenal, Liverpool, Manchester City and overcame Chelsea at the Boleyn on Saturday to lay down a real marker.
The Blues’ form has left the door open for another club to break into the top four and West Ham will have every confidence that they could be that club.