Saints travel to the Emirates Stadium on Wednesday looking to reach a first domestic semi-final since lifting the Football League Trophy in 2010.
But Saints' last major silverware was in 1976 and Frenchman Puel - who joined the club in July after Ronald Koeman left to become Everton boss - believes the current crop of players at St Mary's are talented enough to end the wait.
He said: "I believe (it is possible to win the EFL Cup) with my players - but I do not know if it is possible first time.
"Before I consider winning it, we have to win (against Arsenal). Every game is very difficult.
"The most important objective is to stay qualified in (as many competitions as possible) and we will see in the second part of the season.
"We want to win (trophies), we need to keep our concentration and perform as well as we can and after that we will see."
Southampton travel to London on the back of a 1-0 win against Koeman's Everton and Puel is expected to make a number of changes to his side.
Puel has so far used the competition to give game time to his younger players, something that he thinks will help their development.
But he admits he has to find the right balance between youth and experience against Arsene Wenger's men.
He said: "It is an important game. It is a different competition, it is away at Arsenal and I think that means it is important for the players too.
"It is a good competition to try to win something for the club and I think all my players are ambitious for this competition.
"It is an opportunity for Southampton to win something, we have the ability. It is important to give opportunities for young players to show their qualities.
"It is a balance between getting the result and continuing the work to develop different players and give game time for players without time in the Premier League.
"We started at the beginning (of the competition) with just young players (in the side) and now the teams are mixed of young and experienced.
"I (came to the club) to give young players the opportunity to develop. Southampton have good players in the academy.
"I know my job is to help develop these young players in the academy. These players can improve every time.
"All the players are making progress."