Pompey managed to beat Burnley 2-0 at Fratton Park on Saturday, following goals by Aruna Dindane and Herman Hreidarsson.
Dindane missed a spot-kick in the game.
“One thing I try to teach my players is how to be players with character,” said Grant.
“This is most important and you need a short memory in football.
“You cannot come to half-time crying that you missed a penalty or didn’t play so well.
“You need to see what you can do better and that’s what Aruna Dindane did.
“He missed a penalty in the first half and then he worked harder in the second half than he did in the first. He deserved a goal.”