Tottenham haven't won a leading competition since they beat Chelsea in the 2008 League Cup final.
But Tottenham midfielder Alli is convinced the north London club will finally add to their trophy cabinet this season.
Tottenham are still in the Champions League and FA Cup, and also have an outside chance in the Premier League title race.
But it is the League Cup that presents their first opportunity to end the silverware drought, starting with their last four first leg clash against bitter rivals Chelsea at Wembley.
While the League Cup is often written off as an after-thought for the top clubs, England star Alli is adamant Mauricio Pochettino's team must use the tournament as the catalyst to kick-start a successful period.
League Cup glory would also secure a first major prize for Pochettino, who is widely regarded as one of Europe's brightest young coaches but has yet to win a single trophy in his managerial career with Tottenham, Southampton and Espanyol.
"I think every game, every competition, you want to win it," Alli said. "As players you want to get as far in the cup as we can, hopefully win it. We want to win trophies, that's our aim and we've been playing well. We've been getting quite far in recent years without quite having the finishing product at the end and not getting over the line."
Tottenham crushed fourth tier minnows Tranmere 7-0 in the FA Cup third round on Friday as Pochettino used only three first-team regulars in a bid to keep his key men fresh for the Chelsea tie.
Alli was one of the trio who featured in the rout at Prenton Park and he expects Pochettino's plan to pay dividends against the Blues.
"Some people maybe expect you to prioritise different things, but I believe we've got a strong squad," Alli said. "Players work hard in the gym and on the training field to make sure we're fully fit and the manager makes changes. I think he's very good at that and as players we want to play every game anyway. We've just got to make sure everyone is on it and keep up the consistency because that's the big thing. When you're going into different competitions, you can't take your foot of the gas. You've got to be consistent and keep up your top level."
Tottenham lost the 2015 League Cup final against Chelsea, but have won their last two meetings, including a swaggering 3-1 success in the league at Wembley in November.
Maurizio Sarri's side, who host the semi-final second leg on January 22, will give late fitness tests to Olivier Giroud (ankle) and winger Pedro (hamstring).
Blues boss Sarri is looking for his first trophy in his maiden season in charge.
The spotlight won't just be on the managers, however, amid fears vile anti-Semitic chants could overshadow the tie.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ