The Spireites raced into a 3-0 lead courtesy of goals from Derek Niven, Jack Lester and Donal McDermott, but strikes from Adam Proudlock and Peter Sweeney transformed a comfortable evening into a tense finale for the hosts at Saltergate.
The Mariners remain just above the relegation zone in League Two, and Newell said: "The players responded well after going 3-0 down and we played well for most of the second half.
"We got two goals and might have sneaked one at the end but they are a decent side with a good home record and are probably the best
team we have played away from home this season.
"But we are not firing on all cylinders by any means and getting beat is the worst feeling in the world.
"The way the players responded is something to be pleased about but we are not there yet and we have a long way to go."