A headed goal by last season's leading scorer James Hanson gave City the points in tight game.
"All in all it was a great night for us," said Parkinson. "It was a really tough game. Fleetwood are a very good side. They have one of the best strikers in the league in Jon Parkin, but I thought we handled him well.
"Hanson didn't get the credit he deserved in our 3-1 defeat at Gillingham on Saturday. He ran himself into the ground for us in the heat so it was good to see him score. He led the line great for us and it was a great delivery from Gary Jones. Everyone of his set-pieces was right on the money.
"It was so important to get three points and get the season up and running, settle the new players down and get them used to the crowd.
"It has been a tough start with Gillingham away and Fleetwood at home. I have no doubt these two teams will be up there at the end of the season."
