The Hammers did have to settle for a point against Bournemouth away on Monday night.
However, Fabianski felt the result and the way they performed showed they can turn a corner after a tough start to this season.
He told Premier League Productions: "Coming into this game we knew they are a tough team to play against. They have proved it so many times this year.
"You have to admit that they created many chances tonight. Obviously we wanted to win and a late goal always gives you that feeling that it's almost there. But credit to Bournemouth they were a decent side tonight as well.
"There's always a feeling of disappointment but at the same time playing away from home against a team who has beaten some good teams, it's a good point for us.
"I think we are still trying to work on the aspects of the game the manager is demanding from us. But we are being a bit more consistent. Slowly we are getting there. It's taking a bit longer than what we wanted, but I believe we are going in the right direction.
"So far we have been on and off. We are looking for a bit more consistency. Hopefully we will add a few more results and everyone will be satisfied with the way we play."
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