Despite a disjointed performance after the manager made seven changes to his team, classy finishes from Maya Yoshida and Graziano Pelle secured a comfortably victory well before Scott Sinclair's penalty for Villa deep into stoppage time.
Ambitious Southampton last reached the final of a major competition when they lost 1-0 in the 2003 FA Cup to Arsenal, and, in the knowledge that he has a stronger squad and an improving team, Koeman is confident that an appearance in February's final could prove within reach.
"One of our ambitions is to reach a final, to give our amazing fans an opportunity to go to Wembley and to play for something," the manager said before it was revealed his team would host Liverpool in the last eight.
"That is what every player and manager wants to do, to go to Wembley and fight for a trophy, even the Capital One Cup, because that for us is an important one.
"You know it's difficult
Everybody takes it seriously
I watched the happiness of the fans (of other clubs) yesterday, when the team is winning on penalties, and of the players.
"It is an honour to play at Wembley and to play for a title
Okay, Man City (who on Wednesday defeated Crystal Palace 5-1) has more possibilities to win
But we have shown already we can beat the big ones
We have to be a bit lucky in the draw.
"One of reasons compared to last year when I did not so many changes in the team, in this competition: we spoke about it, we signed more players, our squad is stronger, also in numbers and in the level we need to play."
Wednesday's defeat represented Villa's first fixture since Sunday's sacking of manager Tim Sherwood and Kevin MacDonald replacing him on a caretaker basis.
The latter at the least appeared to inspire improved morale - for the opening 45 minutes they were the superior team and were undermined only by striker Rudy Gestede's poor finishing - but MacDonald regardless believes that securing Sherwood's successor should be their priority.
"It has been quite hectic," he said
"I got a call at 10.30, 11ish Sunday (evening) to be interim
I was disappointed because Tim brought me in
Tim was very good to me
"(It's) probably better for the club (to get a new manager) sooner rather than later so we can get back to doing what we are doing.
"I have not had time to read the news
They have gone down the road of speaking to one or two.
"Sooner rather than later would be better for the club
If they ask me to stay on for Monday's game (in the Premier League at Tottenham) fine by me."
Source : PA