You need to look in SQL Server's error log, which is kind of a catch-22, since you need access to the SQL Server in order to see the error log.
You don't need direct access to SQL Server to read the log; if you have physical access to the machine, you can find the log in something like:
C:\Program Files\Microsoft SQL Server\MSSQL11.SQL2012\MSSQL\Log\ERRORLOG
Right-click, open with Notepad, and scroll to the bottom, you'll see things like:
2013-05-23 16:34:56.29 Logon Error: 18456, Severity: 14, State: 5.
2013-05-23 16:34:56.29 Logon Login failed for user 'whatever'. Reason: Could not find a login matching the name provided. [CLIENT: ]
This is, of course, for security purposes. Similar to the reason why these details are not revealed to the end user when they hit the login failure.