Grant admitted being overwhelmed by emotion when he marched onto the pitch to salute fans after the FA Cup win over rivals Southampton at the end of a week when his club nearly went out of business.
Pompey defeated their neighbours 4-1 at St Mary's, pulling away with goals from Aruna Dindane, Nadir Belhadj and Jamie O'Hara after Rickie Lambert had cancelled out Quincy Owusu-Abeyie's opener.
"I'm very emotional and this is an emotional game," Grant said. "If you win, you make 250,000 other people happy, this is what football is about.
Victory in the fifth-round tie means Pompey have bragging rights on the south coast and go into the quarter-final hat - but the bigger picture is that they have to return to the High Court to fight a winding-up order from Her Majesty's Revenue and Customs.
"I will fight until the last moment," Grant said. "As long as we have a chance on the pitch. What happens in court is out of my hands. If they need to punish someone then it is a person that does something wrong. I don't know who that is but it is not us."