Grayson said: "Our priority is winning League One, but we try to win every cup game that comes along.
"People knock the JPT competition, but it has a final at Wembley and it's every footballer's dream to play there, so it's a massive incentive.
"If we can beat Carlisle over the two legs we will look forward to a good day out, but our performance was average. Over the course of the game Accrington had the better chances and were the better team.
"We kept a clean sheet, but I don't know how. Maybe it was a bit of luck. If we don't improve against Southampton on Saturday they'll punish us."
The first legs of the area finals will be played in the week commencing 18 January, with the second legs to be played in the week commencing 15 February.