Pochettino's side are yet to lift a trophy during his three-year spell in charge and the club has only won two pieces of major silverware in the last 20 years.
Each of those came in the League Cup, in 1999 and most recently 2008, with Spurs beginning a fresh tilt at the tournament on Tuesday, when they host Championship strugglers Barnsley in the third round.
Fernando Llorente is expected to be given his first Spurs start ahead of Harry Kane while another summer signing, the 19-year-old Argentinian defender Juan Foyth, could be handed his debut.
Harry Winks, Kyle Walker-Peters, and Tashan Oakley-Boothe are among the academy graduates likely to be involved but there will be no place in the squad for the talented Marcus Edwards, whom Pochettino likened to a young Lionel Messi last year.
Spurs are 9/1 fifth favourites with Sky Bet to lift the trophy behind holders Manchester United (11/2), Manchester City (6/1), Chelsea (6/1) and Arsenal (7/1) to lift the trophy but Pochettino's quotes might prompt some punters to side with Barnsely at a massive 16/1 to cause a shock inside 90 minutes on Tuesday night or 10/1 to go through.
"The project here at Tottenham is to try to win the Premier League or the Champions League," Pochettino said. For me, that is the two big trophies. Okay, I would love to win the Carabao Cup or the FA Cup for our fans. But Tottenham must build a project with the possibility to fight for the Champions League or Premier League.
"Sorry, first of all it is the Premier League and then the Champions League. If we are going to try to win the Carabao Cup or FA Cup, and forget the Premier League or Champions League, it's a big mistake.
"I think, what it means for a big team to win trophies, is to win the Premier League or Champions League. "There are a lot of examples: in my second season at Southampton, Wigan won the FA Cup. Where is Wigan today, with all my respect? League One.
"Look, that is the most important example - of course, I would like to win trophies but first of all we'll fight for the Premier League or the Champions League."
Despite making major changes, Pochettino will start Dele Alli in a bid to help him rediscover his form after a turbulent start to the season.
"Yes, he is going to play," Pochettino said. "I think he is still very young. His potential is massive. He did very well last season and it's not easy for a young player to keep this level and show this level in every game.
"It is about maturity. It's about finding your balance in training, competing, in your life, everything. The player is not only what we see on the pitch.
"He is not a number. We need to see the player as having a lot of things around them happening. He is not just furniture. There are a lot of things that affect them, that are around them when you are young. I was like Dele, I was from zero to 100. You need to find your balance."
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