The Spurs boss was irked by a post-match question on Wednesday.
Having trailed 1-0 from the first leg of a semi-final encounter, Tottenham found themselves three goals down on aggregate at half-time in Amsterdam.
They, like Liverpool against Barcelona 24 hours earlier, needed a continental miracle.
They found one in the form of Lucas Moura, with the Brazilian forward netting a stunning second-half hat-trick to seal progression on away goals.
Spurs are now readying themselves for a showpiece encounter with Premier League rivals at Wanda Metropolitano on June 1.
The hope is that they will have a full strength squad from which to select in Madrid.
There are, however, still doubts over whether star striker Kane will be ready to come back into contention for an eagerly-anticipated clash.
The England international is currently sidelined with an ankle problem and has been forced to watch on from afar over recent weeks.
He did play some part against Ajax in midweek, with the 25-year-old heading to the dressing room at half-time to deliver a “mental” team talk that inspired his team-mates to raise their game.
He told BT Sport when quizzed on his fitness: “Hopefully [I'll be fit for the final].
“Rehab's going well so far. I started straight-line running this week so that's why I was okay to straight-line run today.
“I didn't want to cut any corners. We'll just see. So far so good. If it carries on the way it should then I hope to be [fit], but there's still a few weeks.”
While Kane was prepared to take questions on his condition, his manager was not so keen.
Pochettino, as can be seen in the video above, stood up and bid “ciao” to the assembled media when pressed on whether he expects a prolific frontman to be back at his disposal against Liverpool.
As a result, the waiting game appears set to continue, with Spurs having just one more Premier League game to come – at home to Everton on Sunday – before taking on Jurgen Klopp’s Reds.