The Magpies fell behind in the first minute when a mistake by Haydn Hollis was seized upon by Lee Angol, who drilled home from range.
Although Alan Smith drew the hosts level, the Stags struck a winner when Branislav Pindroch punched a cross into the path of CJ Hamilton, who chested the ball down and converted from 15 yards.
“I am very frustrated and disappointed because of how cheaply we gave goals away,” Nolan told the Nottingham Post.
“There were a lot of good individual performances, but we just weren’t at the level where we need to be.
“We have lots of work to do and I was disappointed in the manner Mansfield won.
“There wasn’t much in it and I don’t think they deserved to win the game, but I don’t think we did anything to deserve the win either.”
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