The Welsh side could have closed the gap to the play-off places to five points with a win, but Willmott fluffed his lines from the spot to make it a frustrating night for the visitors.
Southend will have been relieved just to take a point, although all three would have moved them into the third automatic promotion spot.
Lee Barnard threatened to grab a debut goal for the hosts early on, but saw his shot from the edge of the box deflected wide for a corner.
County goalkeeper Lenny Pidgeley had to be alert to tip Will Atkinson's header onto the post before the break.
But it was the visitors who spurned the best opportunity of the match after Mark Phillips had brought down Ryan Burge to hand County a penalty.
Willmott stepped up and blazed well wide with 51 minutes on the clock, and the ex-Cambridge United winger was denied redemption when Daniel Bentley made a superb stoppage-time stop.
Phil Brown's Southend are now unbeaten in eight league games, while Newport have not won in five.
