Paulo Di Canio warned Carling Cup second-round opponents Southampton that his Swindon side can beat any Championship opponents after a deserved success at Ashton Gate.
A 71st-minute header from substitute Raffaele De Vita put paid to a poor Bristol City team after the League Two club had dominated.
Di Canio was full of praise for his players.
“If we play like that we can beat anyone in the Championship,” he said. “We showed commitment, quality and determination and should have been two or three up at half-time. When we didn’t take our chances I feared the same thing was going to happen as in our last three games, all of which we lost when we should have won. But in the end we have scored a good goal and allowed Bristol only one clear chance early in the second half.
“I have signed a lot of new players and hope to bring in a new young defender from a Premier club soon, who will give us even more quality.”