Debug Connection Pool Error
I talked to the application team and they say that it has never occurred earlier...so it must be something with database server


Sounds about right =P


  Our SQL server version earlier was SQL 2008 R2 and we migrated to SQL Server 2016


It's likely that, since your SQL Server upgrade, the performance of some of your queries has changed.  This can lead to queries being blocked, or just running for longer (which in turn can cause this connection pooling problem, as you discovered in your investigation).

Have the developers, or users, notify you when they start getting these connection pool errors.  This will give you a time range to look into.

If you have a monitoring tool, use it to look at the queries that were running during that time.  This will give you the queries that need to be tuned.

If you don't have a monitoring tool, try logging sp_WhoIsActive to a table.  There are good step-by-step instructions by Tara Kizer here: Logging Activity Using sp_WhoIsActive – Take 2