Manchester City visited the London Stadium with an excellent recent record at the ground and were tipped to put the Hammers to the sword.
They fell behind in the 18th minute though when Michail Antonio found the back of the net for the hosts and West Ham held the advantage heading into the half time break.
Pep Guardiola brought Phil Foden on at the break and Manchester City pulled level with 51 minutes on the clock when he struck.
They could find no further path through the West Ham backline though and were forced to settle for a draw which means they have picked up just eight points from their opening five league games.
Former England goalkeeper Green believes that teams are no longer taking to the pitch believing they cannot compete with Manchester City.
He said on BBC Radio 5 live: “Disappointing performance for Manchester City, the whole air of invincibility that they’ve had in previous seasons has dripped away.
“They came back in the week against Porto but getting turned over against Leicester was not good and the Leeds game could’ve finished who knows what score, 6-6 or something.
“They’ve not really managed to hit the straps this season compared to past seasons gone by”, Green added.
Manchester City now have to switch their attention back to the Champions League where Marseille will provide the opposition, while next weekend they head to Sheffield United in the Premier League.