Pochettino: Alli injury blow comes at 'worst moment' for Tottenham
With Harry Kane also expected to miss the same period due to ankle ligament damage, and Son Heung-Min away at the Asian Cup, Spurs are without three key attacking players as they prepare to play four matches in the next 10 days, starting with Thursday's trip to Chelsea in the second leg of the Carabao Cup semifinal.
"Now we need to be positive, like with Harry Kane," said Pochettino. "Of course we're going to miss him [Alli] for a long period.
"It's one of the worst moments because we have ahead very busy fixtures. But you know very well us that for us the squad is very important, and it's a very good opportunity for other players to step up.
"Tomorrow [Moussa] Sissoko and Lucas [Moura] are in contention. With [Victor] Wanyama, we'll see if he can be in contention for the weekend in the FA Cup. It's very good news in the last few days to recover Moussa and Lucas, and Wanyama is so close."
Despite Spurs' lack of attacking options, Pochettino has no plans to recall striker Vincent Janssen to his first-team squad.
The Dutchman last played for Spurs in August 2017, and the north Londoners remain keen to sell him for around £15 million.
"I think it's so clear that now it's one year and a half that he's not in our plans," Pochettino said.
"Eighteen months ago we took the decision for him to try to find a different place to play because for different reasons it didn't work. That happens in football -- the relationship between the player and the club doesn't work. You need to find the best solution.
"In the same way we're trying to get him fit as soon as possible - he's training with the Under-23s at the club -- and trying to help him find his best and then trying to find a club where he can be happy again and try to play, but here it's impossible.
"[Our relationship] is very good. I see him in the changing room every day and the restaurant. It's not a personal problem, it's about the professional side. For different reasons that professional relationship isn't working and we need to find a solution."