Frenchman Frederic Piquionne and former Tottenham midfielder Kevin Prince Boateng, from the penalty spot, scored the goals to take Portsmouth back to the cup final for the second time in three years on the weekend they were consigned to the Championship.
England goalkeeper David James also produced the save of the match to deny Peter Crouch at the end of normal time.
Grant said: "We had a belief and the courage to win this game, we knew we could do it.
"They are a good team with a great manager, but tactically we played very well. The players gave their hearts. It was not easy.
"Five players were not 100% and some players did not play in their right position and we did not even have one defender on the bench. In spite of this we played football, scored two goals and I could not ask for more."
It was a good day, too, for Portsmouth administrator Andrew Andronikou, with the club guaranteed £900,000 in prize money for reaching the final, with another £1million coming from television money and gate receipts.
For Grant, however, it was a fairytale after a season of turmoil in which the club was docked nine points for entering administration with debts of more than £70million.
Grant said: "The way we did it after what has happened all this season and to see players give everything and not take the easy solution and not give up and to be in final, it is a crazy day.
"We could write a book about the many things against us this season."
Grant will now lead out his side against his former club Chelsea next month.
"Blues against blues," said Grant. "I'm very happy. I want to celebrate."
He did not forget the Pompey fans who sang themselves hoarse and stayed celebrating for an hour after the match had finished.
"This achievement belongs to the fans and the players," said Grant.
"The players didn't give up. The fans showed how fans need to behave. They were behind the club despite everything. They are so great they deserve it. This club, this year, I will not forget it all my life."
Grant wore an armband to mark Holocaust Day and was due to travel to Poland tomorrow to honour members of his family who died in the holocaust. It made the victory all the more poignant.
He added: "We played like a team, defended like a team and attacked like a team. For this moment you work all your life.
"Every day since I came to this club I needed to answer so many questions about the future, contracts, points deducted, administration. For one day I want to speak only about football.
"I am personally very happy. It has happened again to me to come to a final on Holocaust Day. For me it is important."
He refused, however, to confirm whether he would be unable to select some of his squad for the final because of clauses in their contracts which would cost the club payments.
And he also appeared unaware that Portsmouth do not possess the necessary UEFA licence to play in Europe next season.
Asked if they might apply for it retrospectively he said: "We can do it now? I don't know."