Pompey lost the final against Chelsea 1-0 as Kevin-Prince Boateng had a penalty saved by Petr Cech.
“It was not a fair result, we deserved more,” said Grant.
“We had a penalty at the right time and other good chances. We had a great chance in the first half.
Fought
“I must say it is a sad and very proud day. We played against a team top of the league and we forced them to waste time in the last 10 minutes.
“Chelsea are a good team but I think everyone in Portsmouth can be proud. We played without many injured players but we stopped them playing and passed the ball well.
“We wanted to catch them on the counter-attack. I am very proud of this team and how we fought against a team who have scored seven and eight goals this season against other teams.
“We could have won. Next time I will take the penalty!”