Not able to connect serverless-offline websocket on browser

I have a node project and I have created websocket with serverless and it's running on port 6000.
When I try to connect from wscat it's able to connect

wscat -c ws://localhost:6000.

But when I try to connect from browser using Websocket browser api it fails to connect the connect request is not even reaching the lambda function
On browser I am using

new WebSocket('ws://localhost:6000')
Browser just throws error connection failed with no reason.

When I deploy cloud formation file to aws that websocket I am able to connect

Please help if I am missing anything.