Kane, who has already injured the same ankle this season, was pictured leaving Tottenham's new stadium on crutches after picking up the injury when going to tackle Fabian Delph early in the second half.
Lucas has mostly come off the bench this season, but with Harry Kane ruled out for the rest of the season, the Brazilian has may well have just fought his way into the starting XI.
"He was so upset after the match", said Pochettino.
Pochettino is unsure whether the 25-year-old will be back on the field again before the Premier League season ends on May 12, though Spurs could still be in Champions League contention at that point, with the final of the competition scheduled for June 1.
Spurs confirmed on Thursday that Kane suffered a "significant lateral ligament injury to his left ankle" during their Champions League victory over Manchester City on Tuesday, with a timeline for his return unknown.
Pochettino's men also travel to the Etihad Stadium for the second leg of their Champions League tie on April 17 and it looks doubtful that Kane will be able to play any part.
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And Lucas has claimed his side set the standard to go to Manchester and seal progression to the European tournament's semi-finals. "It's a hard moment for him, and watching the action, we feel so disappointed and it's hard to accept the situation. He will see the specialist this week and we will see".
The win sees Tottenham leapfrog Chelsea into third place and extend their advantage over fifth placed Arsenal to four points ahead of their rivals' matches against Liverpool and Watford.
"The England midfielder will now be assessed to determine his availability for this weekend's fixture against Huddersfield Town".
"Tomorrow 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".
Erik Lamela and Serge Aurier (both hamstring) remain sidelined.