It appeared that County were going to lose the encounter when Luke Chadwick handed visiting Cambridge a 1-0 lead, but Robbie Willmott scored late on against his former club to ensure that the spoils would be shared.
However, despite the fact that his team secured a late point, Edinburgh believes that their performance was worthy of all three.
"We're frustrated because a draw is the least we deserved. We were outstanding and to come away with nothing would have been a travesty, but we're still bitterly disappointed with only taking a point," the official Football League website quotes the former Tottenham Hotspur defender as saying.
"The performances have been improving with every game but we need to be far more clinical in front of goal because that's the only thing letting us down. We've had a shot off the line, one great save and hit the bar, but we know we have to be converting those opportunities."
The draw moved Newport up to 19th in the League Two standings.