The Magpies dominated the clash but had to wait until midway through the first half to make the breakthrough through Ronan Murray.
Jake Cassidy doubled the tally in the second half and Cox claimed his side did not show enough bravery and commitment to challenge their local rivals in the 2-0 defeat.
"They seemed to have an extra drive in them in the way they worked with the ball and without it," Cox said.
"I'm fuming really. We've lost a local derby and Notts County thoroughly deserved the win. We need bravery in the last third of the pitch and to get on the ball and have shots at goal.
"We started well, but as the game wore on they ground us down which is something we are very good at ourselves.
"I just thought they were better at what they did than we were. I wouldn't say we paid them too much respect, but the boys need to understand when we do what we are good at we are hard to handle.
"We've switched off for two goals and allowed them to stroll through us without any stubbornness, but we never had that in this game and it's disappointing."
Reece Brown, the on-loan Birmingham winger, came close to adding to Murray's goal before the break when he sent a firm header just wide of the post.
Mansfield's threat was limited, but Alex Fisher did force a save from Fabian Spiess early in the second half as they looked for an equaliser.
Notts County assistant manager Greg Abbott said the win somewhat made up for the last-minute defeat suffered at home to Bristol City on Sunday.
"The performance is always the thing you look for in terms of progression," he said. "I thought we passed it well, as we have done all season.
"Reece Brown was in a great role as defenders don't know which player to pick up. He got away from his marker and created some chances for us in the first half and he makes us play attractive football.
"Ronan has shown himself as being brilliant with his goalscoring record. The build-up to the goal was fantastic and that allows us to play good football.
"It's difficult against Mansfield as they've got some big, strong boys and they get the ball forward quickly.
"We had to compete and battle away and in this game we did that, getting key players on the ball in the first half."