Jordan Lyden's second-half strike ended Newport County's EFL Trophy campaign at the group stage.
A much-changed County side thought they had conceded a penalty in the 16th minute when Nick Townsend brought down Lyden in the box and the referee blew his whistle and pointed to the spot.
After some protestation though, the official changed his mind and it looked the correct decision the second time around as it appeared Townsend won the ball fairly in the initial challenge.
A first half of few chances saw Alex Gilbert have a shot deflected wide for the hosts on 21 minutes before Timmy Abraham shot wide from a tight angle two minutes later.
Gilbert and Jayden Mitchell-Lawson both flashed efforts past the post for Swindon but the half closed out with Newport coming closest to scoring with Lewis Ward doing well to push an Abraham header over the bar.
A header was the first major chance of the second half for County too, with Kevin Ellison this time nodding wide after a good cross from the right by Lewis Collins.
It was Swindon who took the lead though on 57 minutes when Robins captain for the evening Lyden scored a rebounded effort from the middle of the box after Townsend palmed a Mitchell-Lawson effort into the path of the Australian midfielder.
County needed a goal to reach the knock-out stages of the EFL Trophy but Swindon looked more likely to score next, with Harry Parsons shooting over and Townsend was called into action to superbly deny Mitchell-Lawson with a dive to his left when Mitchell-Lawson looked certain to score from close range.
The game finished with Harry McKirdy hitting a free-kick straight at Townsend in second-half stoppage time and County now just have the league to focus on for the rest of the season.
Swindon Town: Lewis Ward, Jordan Lyden (C), Harry McKirdy, Jayden Mitchell-Lawson, Alex Gilbert, Rob Hunt, Ryan East, Harry Parsons, Mo Dabre, Harrison Minturn, Callum Winchcombe
Subs not used: Stephen Mildenhall, Donnell Gordon, Levi Francis, Anton Dworzak, Harvey Fox, Thomas Wynn-Davis, Jedidiah Afenyo
Newport County: Nick Townsend, Ryan Haynes, Ed Upson, Matt Dolan (C) (Joe Woodiwiss '61), Jermaine Hylton (Louis Hall '75), Alex Fisher, Timmy Abraham (Jordan Greenidge '58), Lewis Collins, Kevin Ellison, Chris Missilou, Harrison Bright
Subs not used: Lewys Twamley, Evan Ovendale, Callum Ryan-Phillips, Anuerin Livermore