Alderweireld played the full 90 minutes of Saturday's 3-1 win against Fulham after being left out for the 2-1 victory against Newcastle United last weekend, while Rose and Sissoko were unused subs at Wembley.
Asked specifically about the future of Alderweireld after the match, Pochettino spoke uninterrupted for six minutes about what he expects from those in his squad, and vowed that he would not be "blackmailed" by any unhappy players.
"I won't talk about him; I'll talk in general always," he told reporters. "I want players committed with the team. Players that are not happy, from my point of view, can leave. Then it's different if they can negotiate with Daniel [Levy, the Spurs chairman] or not. But I want players who are fully committed with the team and want to fight for the team. The players that are here are all committed.
"Not one told me today that they wanted to find a solution. Today, I am so open to listen to players if they want to leave. But if they are going to be here, I want full commitment. If not, tomorrow we can find a solution. I am so tired talking about this. If I am here, in my position as manager, because the club trusts in my decision, not because I am so handsome... maybe that too!
"I understand every single situation, I understand agents, I understand that football is a big business too and people protect their assets and duh duh duh, daa daa, doo doo too! You're not going to put pressure on me, or put pressure on my decision. Nobody is going to blackmail me.
"The club is not going to put pressure on me or I'll go home. When I started playing football it was because I loved the emotions. When I started my career as a manager it was to provide the players with the tools to play and enjoy football on the pitch. But sometimes it is so tough, but that is part of my job too, I understand."
Spurs became the first Premier League club to not make a summer signing since the current transfer window system was adopted in 2003.