But Curbishley pointed to how well Town performed and wished them luck for the season.
"Grimsby tonight belied their league form and gave us a real scare," he said after the game.
"I think they played tremendously well and I hope it gives them a bit of a lift in terms of their league performances.
"They have had good results here at home and we always knew it was going to be a difficult game and we were right.
"They put us under tremendous pressure, created a couple of really good chances - but they didn't take them and we took ours.
"I'm glad to get out of the game with a result and be in the next round.
"We have had a tough old night and it reminded me of the games we've had over the years against Grimsby, because they have always been real tough games here.
"They attacked it and really did well."
Curbishley also revealed his affection for the Mariners.
"I just hope they can carry on the form they showed tonight," he added.
"We have got a bit of affection for Grimsby.
"I've just been talking to Clive Mendonca, and we lent them couple of players a couple of seasons ago in Martin Pringle and Andy Todd which helped them out.
"There's a relationship there and I do hope they start picking up more points away from home and shoot up the league."