Swindon's best chance in the first half fell to Brian Howard's who had his shot mid way through the half hit the post. Alan Reeves should then have put Swindon 1-0 up minutes later when his header was well saved by former Swindon 'keeper Frank Talia.
Wycombe took the lead a minute before half time when another ex Swindon player Andy Thomson headed in a cross to make it 1-0.
On 64 minutes Wycombe then made the scores 2-0 with a goal straight from a free kick.
Andy Gurney pulled a goal back on 70 minutes with a penalty after Sam Parkin was tripped in the area. After the penalty Swindon then came close to making it 2-2 hitting the post for the second time in the afternoon.
But it was Wycombe who made the most of their chances making it 3-1 on 85 minutes with a goal from Darren Curie. Swindon keeper Rhys Evans protested that he had been fouled, and also Wycombe had looked like thy could be offside, but the goal was allowed to stand.
On 87 minutes Wycombe made sure of their place in Round 2 with a close range goal from Jermaine McSporran sending most of the 1,127 travelling Swindon fans home unhappy.
Overall Swindon were fairly poor with Mooney and Parkin both having quiet games, but Swindon did not deserve the lost 4-1. With 10 minutes to go Swindon looked like they might at least snatch a draw, but in was Wycombe who went into the draw for Round 2 where they were drawn at home to Division Three side Mansfield Town.