Keane is notoriously hard to please and rarely hands out plaudits readily, but he joined the chorus of acclaim for Pochettino and his players.
"It was a very good performance from Tottenham, I though they were excellent, and we are not surprised at this stage," stated the Ireland assistant manager.
"This is a huge boost for Tottenham, for their confidence and self belief. They were fantastic and it is the best feeling in the world when you can win a football match like that. To turn over Real Madrid as comfortably as they did tonight, it can only breed confidence throughout the whole club."
Keane's praise for Spurs was contrasted by his scathing criticism for reigning European champions Real Madrid, as he suggested they were lacking in focus from the first whistle.
"They didn't seem at it," added Keane. "Their body language was not right and while they don't have that quality to hurt you, without the ball they were shocking in terms of closing people down. The decision making from world class players were poor, but Spurs still had to be good enough to take advanatge."
Meanwhile, Spurs boss Pochettino believes his team belong among Europe's elite after they blew away Real Madrid to qualify for the Champions League knockout stages.
Spurs followed up a 1-1 draw a fortnight ago with a superb performance against the competition's defending champions at Wembley and ran out 3-1 winners courtesy of Dele Alli's double and a strike from Christian Eriksen.
"You've all seen today that Tottenham is a big team; we're playing at Wembley in front of 80,000 people and these are really historic occasions.
"We now belong in and among the best, not only in England but in Europe, and results like this help people to see that this is where we are going."