Their 2-0 defeat of Crystal Palace on Wednesday ensured their progress to the competition's fourth round, where they will host Sunderland, and at least one further fixture to an already busy schedule.
Three victories in the past week have been notable not only for the fact they were the first of Puel's reign as manager
He also rotated his team across the three competitions, highlighting the strength in depth from which he can take confidence.
Another summer in which high-profile players like Victor Wanyama, Sadio Mane and Graziano Pelle departed, in addition to Puel's predecessor Ronald Koeman, led to pessimism surrounding their chances this season.
They continue to impress, however, despite the manager making changes throughout his team.
Charlie Austin scored again on Wednesday having not made the starting XI against Swansea on Sunday, while Jake Hesketh scored his first senior goal on his first appearance since December 2014.
Speaking to Southampton's official club website about his increasing options, Puel said: "It's very interesting for the players and this squad.
"If my players keep this very good attitude and spirit, and we can move the team around to keep our energy, this bodes very well for the future.
"All the players played a very good game, with quality on the ground and many chances.
"We gave game time to other players like (Harrison) Reed, and Hesketh
It's important for us to improve all these young players.
"It gives many possibilities and answers for the future.
"We will see the future
It's important to continue and to play all these competitions.
"Now we must focus and go to play West Ham (next in the Premier League), which is a very difficult game."
Palace await news surrounding their captain Scott Dann after he was substituted in the 19th minute with a suspected hamstring injury.
His departure proved the point at which Southampton took control of play, but in his potential absence their manager Alan Pardew was confident of James Tomkins' chances of recovering his fitness for Saturday's fixture at Sunderland.
Damien Delaney deputised for Tomkins at Southampton, and is line to play alongside Tomkins should Dann be ruled out, and Pardew said: "Damo, (Lee Chung-yong) and the goalkeeper (Wayne Hennessey) were all terrific in a team that was disjointed towards the end.
"I actually thought Damo was our best player."
Source : PA
Source: PA