That is according to former Tottenham and Republic of Ireland striker Robbie Keane.
Spurs boss Pochettino is the favourite to become the next permanent Manchester United manager in the summer, while Real Madrid have also been mooted as suitors.
The Argentine is yet to win a trophy at the north London club but has exceeded many people’s expectations with the transfer budget he has at his disposal.
Pochettino has admitted Spurs need to spend more if they want to compete for the major honours.
Keane was in the Tottenham team when they last won a trophy back in 2008.
He concedes his former side need to win some silverware but can see that task made harder if Mauricio Pochettino leaves.
“Yes they do [need to win a trophy],” Keane said on Sky Sports.
“When people go on about it quite a lot it certainly gets into people’s heads.
“Tottenham are on the verge of doing something big I think, in the next few years.
“If they lose this manager, it’s going to set them back a few more years.
“You don’t want to do that because in the last few years under Pochettino, he’s been incredible.
“He’s a fantastic manager and listen, when you’re as good as him, of course there’s going to be big teams come for you.
“But Tottenham’s a massive team, new stadium coming.
“I fancy them tonight to win and the second leg.
“If they win a cup I think that will just set the ball rolling for them.
“Keeping this manager is a key factor in that.”
Tottenham beat Chelsea 1-0 in the EFL Cup semi-final first leg on Tuesday night to maintain their push for a first trophy under Pochettino.
Harry Kane scored the winner after a VAR decision saw the England striker awarded a penalty for a foul by Chelsea goalkeeper Kepa.
The two sides play in the reverse fixture at Stamford Bridge on January 22.
Chelsea must play Newcastle and Arsenal between that second leg, while Spurs have games against Manchester United and Fulham to come.