Tottenham need four points from their remaining three matches to ensure Antonio Conte's defending champions don't overtake them for fourth place.
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And Pochettino told Sky Sports: "I think it was a good night for us".
"It was a must-win game - so important for us". I am very happy because the three points now put us in a very good position. We could have played better in the first half, could have moved it a bit quicker and we were lucky to be ahead thanks to Hugo [Lloris].More news: Russian President, South Korean Leader Discuss, Praise Korean New Deal
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"During the whole season, 10 months, it is hard to keep playing good football".
"The team came back from a hard loss". I'm looking forward to the last three games.
Kane's clinching goal allowed him to close in on Mohamed Salah as the two vie for the Golden Boot, albeit the Liverpool forward remains the clear favourite to end as the league's top scorer.
"That's 150 Premier League games and 105 goals", the Tottenham manager said.
It was his fifth goal in the last eight games as he continues to respond well to being overlooked by Southgate during the last global break.