Hugo Lloris, Dele Alli and Moussa Sissoko had already been ruled out of Tuesday's match through injury.
Having sat out Saturday's 2-1 home loss to Liverpool in the Premier League, all three players will not feature in Milan.
And Pochettino revealed on Monday that, despite not carrying any injuries, Alderweireld and Trippier will also miss out.
"We still have out Hugo Lloris, Dele Alli and Moussa Sissoko," Pochettino told reporters.
"They are in London. They are on the list with players like Foyth and Nkoudou. Then a technical decision in London - Toby Alderweireld and Kieran Trippier .
"It’s a technical decision. You can look it up in the dictionary. Tactical? That is on the pitch, although I guess you could say this is tactical off of the pitch."
Lloris is expected to be out for "several weeks" with a thigh injury but Alli's hamstring problem, sustained on international duty with England, is less serious.
Sissoko also has a hamstring injury and will not be available for the San Siro fixture, the first for both teams in Group B.
Both Inter and Spurs will be hoping that continental cheer can raise their spirits after disappointing starts to the domestic season.
Tottenham lie sixth in the Premier League with three wins and two defeats so far, while the Italians languish down in 14th having won just one of their opening four games.