Jewell rested several first-team regulars at Blundell Park, putting his faith in the fringe players in the squad.
But they failed in the main to deliver, much to the disappointment of the manager who had hoped to make progress in the competition.
A first-half goal from Andy Parkinson put the Mariners into the hat for the second round draw tonight, and Jewell admitted Russell Slade's side deserved their victory.
He said: "I'm very disappointed. We came and made a few changes but credit to Grimsby, they deserved it.
"Their players showed more hunger than ours and that was the biggest disappointment for me on the night.
"Grimsby could have been more than 1-0 up at half-time while we were toothless.
"This season we have been creating plenty of chances, but last night we didn't create enough for the amount of ball we had.
"It just goes to show that if your attitude is not quite 100%, you certainly won't win football matches.
"I was disappointed in the manner of defeat.
"We tried a different shape which didn't work, and some of the fringe players had the opportunity to impress me but didn't do too well.
"I'd rather we lost last night than on Saturday at Sunderland, but winning is a good habit to have.
"I'm not going to beat myself up over this, but not too many of the lads who came into the side did themselves justice like I know they can.
"Being fair to them, it is hard being out of the team, and for a lot of players, it was their first proper 90 minutes since last season.
"You can't expect them to do fantastically well, but I expect them to do better than that.
"We huffed and puffed, David Graham missed a sitter near the end, but Grimsby had one or two good chances as well."
Jewell is now targeting the visit to the Stadium of Light for Latics to bounce back to form, albeit with a much changed side.
He left seven regulars out of the starting line-up last night and all of them – fitness permitting – can expect a swift return to action in Wearside.
The manager said: "I'm disappointed we're out of the Carling Cup because the side we put out was still capable of winning the game.
"But it might be a blessing in disguise. We have a lot of games coming up and we haven't got the biggest of squads here which is my choice.
"We have to try and take positives out of this defeat and playing Sunderland away is the most important thing for us now."