Alderweireld sustained the injury against Real Madrid on November 1 and the Belgian is now expected to miss another eight weeks of competitive action.
It means the defender is likely to sit out crunch Premier League games against Manchester City and Manchester United but could return in February for matches against Liverpool and Arsenal.
Spurs then face Juventus in the first leg of the Champions League last 16 on February 13.
“We cannot change the reality. The reality is that he is injured and cannot play until February,” Pochettino said, ahead of tonight’s clash with Brighton at Wembley.
The Argentinian insists Alderweireld’s absence would not push him to look for defensive additions in the January transfer window.
Serge Aurier and Ben Davies are both capable of playing more centrally, while 19-year-old Juan Foyth could be promoted.
Eric Dier is likely to continue alongside Jan Vertonghen against Brighton as Davinson Sanchez is serving the second part of a three-match ban.
Pochettino also addressed the bust-up that followed Manchester City’s win at Manchester United on Sunday. He said scuffles between players in the tunnel are not unusual.
“In France too they were tough, playing (for Paris St Germain) against Ajaccio at half-time I remember a massive fight in the tunnel,” Pochettino said.
“You didn’t see but there was fighting between us. It was terrible. Sometimes it happens.
“Was I hurt? No, I was clever. It was tough. After you are scared a little bit because it was like we were animals fighting and you do not know what happened. I don’t know if it was similar.
“You can talk when you’re calm and relaxed, but when something happens on the pitch and you are under stress and emotion sometimes you cannot stop and it can happen.”
As well as Alderweireld and Sanchez, Spurs will be without Victor Wanyama against Brighton as the midfielder has only just resumed light training after his knee injury. Erik Lamela, who recently recovered from a year-long hip problem, is in contention to start.
Meanwhile, Brighton boss Chris Hughton says it is important his players react when they tackle Spurs this evening. The Seagulls have suffered losses against Liverpool and Huddersfield, conceding seven goals in the process.
“It’s important we react, and one thing we’ve tried to do throughout the season so far is to make sure that everybody is level-headed — both the players and everyone around the club,” Hughton said.
“It’s disappointing that over a two-game period we’ve conceded seven. The manner in which we conceded against Huddersfield was disappointing, but if we think we have done something poor then we have to make sure it’s better on Wednesday.”
Spurs are fresh from a 5-1 thumping of Stoke, but Hughton says his players will relish the challenge.
“They are a top-six side, and if you are not on it you will be punished. But it’s a challenge to look forward to, and a majority of our players haven’t played at Wembley Stadium, and that’s the wonderful challenge for them as well.
“We have to have the right balance. If you defend for 90 minutes, then the inevitable will happen at some stage and they will open you up and score. We have to have periods where we have good possession and show that we can be a threat.”