Despite the team's improvement under the last couple of years, Spurs have not won a major trophy since 2008, when they lifted the League Cup.
Mauricio Pochettino's side will begin their EFL Cup challenge against Barnsley on Tuesday night, and Son has revealed that Tottenham will take the competition seriously as they bid to land silverware.
"I can see in their faces how hungry the players are," Son told the London Evening Standard. "Everyone's ready for the League Cup, the Champions League, the Premier League and the FA Cup when it starts.
"In all competitions we have to get as far as possible, and we're just looking forward to winning this game. It's difficult to say 'we're going to win the League Cup'. It's much easier to say than to do it and in football you never know what's going to happen. That's why on the pitch we need to be there in every competition.
"I'm a person that wants to win every game. When I don't, when I draw, I'm very disappointed, like on Saturday. Let's see what happens on Tuesday."
Tottenham will enter the clash with Barnsley off the back of a goalless draw at home to Swansea City in the Premier League.