While they will be without Kane and Alli, there are no other new injury problems for Pochettino to deal with.
"We need to assess him this afternoon and I am not too optimistic", the manager said.
Kane suffered the injury following a challenge from Fabian Delph.
Pochettino did not allude as to whether surgery would be needed but did say Spurs have plans in place for Kane's recovery.
Lucas Moura scored a hat trick as Tottenham stayed on course for a top-four finish in the Premier League by beating Huddersfield 4-0 on Saturday.
Pochettino's men are fourth in the league and are one point clear of fifth-placed Arsenal and three points ahead of sixth-placed Manchester United.
"Pochettino added: "[It] is not a game to rest players but we have a lot of players who played 90 minutes (against City) who maybe aren't in condition to play for different reasons.
"Nobody should feel that we don't care about what happened in the last few months".
"We need to assess him every day, but we need to have proper answers to see when he can possibly start training with the team".
Meanwhile the likes of Serge Aurier (hamstring), Eric Dier (hip flexor) and Erik Lamela (hamstring) are out of the Huddersfield fixture.