Unable to connect to Home Assistant - port problems?

My HA instance is accessed via subdomain and reverse proxy on the server (via HTTP 80 port on the web side and HTTP 8123 port on the HA virtual machine side.
In the ordinary web (mobile network as example) I can access my HA without any problems.
Trying to access HA from my workplace. Our firewall allows only packets going to 80 and 443 ports. It seems to work…
But! When I access my HA, I see login page and enter credentials… After that I catch an error:

Unable to connect to Home Assistant. Retrying in 60 seconds…

Whats the problem? How to solve it?

You need to catch the error written in the logs on the HA installation.
It might tell you more detailed what went wrong.

Proxy both http and websockets. it is often the websockets that are forgotten.