Jones, who replaced Ralph Hasenhuttl as Southampton boss in November, endured a difficult start to his reign, losing four of his first five matches in charge, and many were questioning whether he was the right man for the job.
However, the 49-year-old has since recorded back-to-back victories in the domestic cups, with a 2-1 FA Cup win against Crystal Palace on Saturday followed by their EFL Cup success over Man City.
First-half strikes from Sekou Mara and Moussa Djenepo put Southampton in control and their resilient performance at St Mary's prevented Pep Guardiola's side from registering a single shot on goal for the first time since April 2018.
Ward-Prowse, who played the full 90 minutes in an advanced midfield role, believes that Jones has had a positive impact at Southampton and hopes they can now replicate their domestic cup form in the Premier League, where they currently sit rock bottom of the table.
Speaking to Sky Sports, Ward-Prowse said: "A special night. These games are special to play in especially when you're struggling in the league. We knew this was a distraction from the league and a great showcase. We showed no fear.
"It's always tough when you're in the position we are. The manager has been excellent and has given us fresh ideas and new energy. He wanted us to be bold and aggressive.
"We have been guilty in the past of having a result at half time and dropping off. We showed a different part of our game. We thoroughly deserved the win.
"That's the challenge now (taking their cup form into the league). To put in a performance like that means nothing if we don't get anything from Everton.
"It's massive. For the whole team. We've worked so hard under the new manager on being hard to beat. We need to be a hard team to play against. On the back of the last two results we can take momentum into the game on Saturday."
Jones expressed his pride after beating Man City, adding: "I'm really proud of the players, of myself and the coaches. We've gone through a lot recently, people questioning a lot of things. That goes a little way to justifying why we're here and what team we're trying to create.
"I'm really proud of the club tonight and how we've come through a tough time. It was the second cup win in a week and shows we're building something.
"The performance levels have been there in the last four games but we've given silly goals away and not giving ourselves a chance.
"Tonight we were excellent. It's been building. I've had three Premier League games. I only had one day to prepare for Liverpool, I'm not David Blaine. I understand people's frustrations but we're building. Rome wasn't built in a day. We are on the way.
"We want to be hard to beat. This has to be our benchmark, the level we attain to. We had a lot of good situations today. It's a step in the right direction."
Southampton have been drawn against Newcastle United in the EFL Cup semi-finals, with the first leg to take place at St Mary's on either January 24 or 25.
Jones and co will look to move off the foot of the Premier League table with a victory against Everton at Goodison Park on Saturday.