The meeting with a side 34 league places above them has been described by Di Canio as "the main event" and the Italian made a number of changes to his team at Stevenage in Saturday after admitting the chance to beat Paul Lambert's side took precedence.
And that trip to Broadhall Way saw a convincing 4-0 victory despite a number of selection changes with one eye on the visit of Villa.
Simon Ferry, Gary Roberts, Jay McEveley and James Collins, the hat-trick hero against Stoke, were all on the bench and despite their absence Swindon put in one of their best displays of the season against Gary Smith's men who had not lost at home for 18 games.
Di Canio is looking for his side to claim a third Premier League scalp after they followed up their FA Cup defeat of Wigan last season with victory over Stoke in the second round of the league cup in August.
"All the attention must now go to Tuesday night and Aston Villa," Di Canio told the Swindon official website.
"We have won two games against Premier League teams and now we have a chance to take on another side.
"We must stop thinking about the league now and take an extra lift to try and make something special on Tuesday night.
"I did save some of the main players and we moved things around. I tried to handle the situation and go out in the second half to win the game, with one eye on Aston Villa.
"The game on Tuesday is now the main event for us."
Di Canio's men are not short of confidence for the sold-out visit of Villa, who have only won two of their last 25 league games, having knocked out Championship sides Brighton and Burnley as well as Stoke at the Britannia - their best run in the League Cup since reaching the semi-finals 17 years ago.
Villa, who have just one win and seven goals from their nine League matches this season, have not lost to a third-tier club since 2005 when Doncaster ran out 3-0 winners at this stage of the competition but they will not be getting carried away ahead of a trip to the County Ground where Swindon have lost just twice in all competitions since August 2011.
The Robins will be without one of Saturday's star performers in playmaker John Bostock who hobbled off with a groin injury.
The Italian's options could be boosted by a return to the squad for striker Andy Williams who has not featured since October 6 with a calf injury. Nathan Thompson could also be available after recovering from an ankle problem.