Unai Emery’s team head to west London on Tuesday night for a third round tie, seeking just their second win in the competition since the Spaniard took charge.
Villa, who have not won a major trophy since 1996, reached the semi-finals of the Conference League and FA Cup in the past two seasons.
Mings, a member of the team which reached the Carabao Cup final in 2020 under Dean Smith, is desperate to end the long wait for honours.
He said: “Obviously, we’ve had some relative success in getting to the Carabao Cup final a number of years ago, so we want to try and go as far in these competitions as possible, and the FA Cup obviously will add to that in January when it starts.
“Hopefully, we can go far in as many different competitions as possible, and silverware has to be the goal.”
Villa also start their Europa League campaign next week when they host Bologna in the first match of the group stage.
Emery’s men are yet to score a goal this season and have taken just two points from their first four Premier League matches but Mings, who signed a new contract in the summer, is excited for what is ahead.
He said: “I love it. I take a great deal of pride every time I play in this shirt, every time I turn up to work.
“There’s been some good times here and some not so good times. It’s been a long time, but I absolutely love it.
“I still have the same drive and determination. (I’m) here for the challenge and I’m definitely aligned with the other players that have been here for a long time now, that silverware is the next goal.”