The 46-year-old Argentine remains focused and upbeat even though Kane likely to be missing until March while Alli is being assessed after going off late in the 2-1 win over Fulham on Sunday with a hamstring problem, AFP reported.
Pochettino is also without South Korean forward Son Heung-min, who is away on Asian Cup duty.
Pressure is growing on the manager and his talented young Spurs side to translate attractive football into silverware – a loss in the 2015 League Cup final and two FA Cup semifinal defeats have led to questions over their mental strength.
Spurs take a 1-0 lead into Thursday's second leg at Stamford Bridge against Chelsea, which beat them in the League Cup final and the 2017 FA Cup semifinal.
"I am so optimistic," Pochettino was quoted as saying in the Daily Mirror. "We are going to prepare for Chelsea, try to find solutions. Try to be solid, aggressive, offensive and keep our identity.
"Of course it's going to be tough. I don't say we're going to win easily on Thursday. But we are going to try.
"That is the most important thing and I know that afterwards I will be happy because the squad we have is going to give their best to be in the final."
Pochettino, who is one of the frontrunners for the permanent job at Manchester United and has also been linked with Real Madrid, believes his players have learned to shake off adversity better.
"More problems, more positives, more optimism," he said. "In football, you cannot be affected by the things that happen.
"When the game finishes you can be disappointed and all the emotion arrives, but during the game the most important thing is that the team isn’t affected by that situation."