The Magpies host the League One side at Meadow Lane on Sunday afternoon and the boss is hopeful that a break from the league campaign could be the perfect tonic for his side following their recent difficult run.
He said: "Our main objective is to succeed in the league but the FA Cup has the attraction of helping us financially and giving the players an opportunity to test themselves against Premier League opposition.
"I get excited as a manager in the same way the supporters do. If you're in the hat for the third round there is always a buzz about who you might get and that is what makes the FA Cup so good.
"If we can get the result we want and get through to the next round it will give us a lot of confidence."
In order to make it into the draw on Monday night, the Magpies will have to overcome a side who have won five of their last six games to cement themselves in the League One play-off places.
"We have to respect Peterborough; they are a good footballing side and they are going well in League One," Sheridan said.
"We have to be on the front foot and not allow them to dictate the game, show a bit of endeavour and a willingness to win.
"If we show all of that, the supporters will get behind us because they have done it before this season.
"A win could help us get out of the little rut we're in at the moment. I do believe we will turn the corner soon and it would be nice to start that with a win against Peterborough."