Grant suffered a 4-1 home defeat by Manchester United on Saturday in his first game in charge.
Pompey are rock bottom of the Premier League after having lost 11 of their 14 league games this season.
Grant said: “I have spent 90 per cent of my career at the top of the table and I don’t have enough experience in the bottom of the league.
“But I knew what was coming when I took this job and even if we are in a difficult situation, miracles do happen sometimes.
“I am an optimist by nature and there are still more than 20 games until the end of the season. But it will not be easy and it is a big challenge for me, for the players and for the club.
“It was not my life’s dream to take charge of a team at the bottom of the table but I have a job to do and I am going to do it.”
