Kevin Dawson gave the Glovers the lead when he forced Adam Collin into a mistake amid claims the goalkeeper was fouled in the build up, before Otis Khan then made it 2-0 after Ryan Hedges' shot was parried away by Collin.
"It is disappointing start because you want to hit the ground running as quickly as you can," Sheridan said.
"The two goals have cost us the game. We started okay in the first five minutes and we were never in any danger, but they've had a good chance before they scored.
"I don't actually think we played that bad, but you can't start playing when you are 2-0 down.
"The opposition are going to sit back and try to consolidate the lead. But the goals we conceded were very poor.
"You can't concede goals like that. It was an uphill battle although I thought we had a go in the second half.
"We took the game to them, but I was disappointed because you want to get something from your first game."
What do Notts need to do ahead of Tuesday's meeting with Scunthorpe? Let Pride of Nottingham know your thoughts by signing up to the website, visiting the forum and joining the conversation.